LMFDB - Embedded newform 27.2.e.a.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,2,Mod(4,27)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("27.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	27.e (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.215596085457$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			7.1
Root			$0.500000 + 1.27297i$ of defining polynomial
Character	$\chi$	$=$	27.7
Dual form			27.2.e.a.4.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.57954 + 0.574906i) q^{2} +(1.45446 + 0.940501i) q^{3} +(0.632343 - 0.530599i) q^{4} +(-0.196143 - 1.11238i) q^{5} +(-2.83808 - 0.649381i) q^{6} +(-2.99441 - 2.51261i) q^{7} +(0.987144 - 1.70978i) q^{8} +(1.23092 + 2.73584i) q^{9} +O(q^{10})$	\(q+(-1.57954 + 0.574906i) q^{2} +(1.45446 + 0.940501i) q^{3} +(0.632343 - 0.530599i) q^{4} +(-0.196143 - 1.11238i) q^{5} +(-2.83808 - 0.649381i) q^{6} +(-2.99441 - 2.51261i) q^{7} +(0.987144 - 1.70978i) q^{8} +(1.23092 + 2.73584i) q^{9} +(0.949332 + 1.64429i) q^{10} +(-0.324801 + 1.84204i) q^{11} +(1.41875 - 0.177016i) q^{12} +(0.688417 + 0.250563i) q^{13} +(6.17430 + 2.24726i) q^{14} +(0.760915 - 1.80239i) q^{15} +(-0.862951 + 4.89404i) q^{16} +(-0.944822 - 1.63648i) q^{17} +(-3.51713 - 3.61372i) q^{18} +(-1.37143 + 2.37538i) q^{19} +(-0.714260 - 0.599335i) q^{20} +(-1.99214 - 6.47073i) q^{21} +(-0.545962 - 3.09631i) q^{22} +(-4.46428 + 3.74597i) q^{23} +(3.04382 - 1.55840i) q^{24} +(3.49954 - 1.27373i) q^{25} -1.23143 q^{26} +(-0.782746 + 5.13686i) q^{27} -3.22668 q^{28} +(4.99910 - 1.81953i) q^{29} +(-0.165691 + 3.28441i) q^{30} +(1.02696 - 0.861722i) q^{31} +(-0.764882 - 4.33786i) q^{32} +(-2.20485 + 2.37370i) q^{33} +(2.43321 + 2.04170i) q^{34} +(-2.20765 + 3.82376i) q^{35} +(2.23000 + 1.07687i) q^{36} +(-1.69806 - 2.94112i) q^{37} +(0.800605 - 4.54046i) q^{38} +(0.765621 + 1.01189i) q^{39} +(-2.09556 - 0.762721i) q^{40} +(-1.68800 - 0.614382i) q^{41} +(6.86673 + 9.07549i) q^{42} +(0.873477 - 4.95373i) q^{43} +(0.771999 + 1.33714i) q^{44} +(2.80187 - 1.90587i) q^{45} +(4.89793 - 8.48346i) q^{46} +(1.30892 + 1.09832i) q^{47} +(-5.85798 + 6.30658i) q^{48} +(1.43775 + 8.15389i) q^{49} +(-4.79539 + 4.02381i) q^{50} +(0.164904 - 3.26880i) q^{51} +(0.568265 - 0.206831i) q^{52} +2.84494 q^{53} +(-1.71683 - 8.56388i) q^{54} +2.11276 q^{55} +(-7.25193 + 2.63949i) q^{56} +(-4.22874 + 2.16507i) q^{57} +(-6.85023 + 5.74803i) q^{58} +(-1.95529 - 11.0890i) q^{59} +(-0.475188 - 1.54347i) q^{60} +(4.00710 + 3.36235i) q^{61} +(-1.12672 + 1.95153i) q^{62} +(3.18824 - 11.2850i) q^{63} +(-1.26751 - 2.19540i) q^{64} +(0.143694 - 0.814930i) q^{65} +(2.11800 - 5.01694i) q^{66} +(1.77511 + 0.646086i) q^{67} +(-1.46577 - 0.533495i) q^{68} +(-10.0162 + 1.24972i) q^{69} +(1.28877 - 7.30898i) q^{70} +(6.09193 + 10.5515i) q^{71} +(5.89280 + 0.596074i) q^{72} +(-4.94384 + 8.56298i) q^{73} +(4.37302 + 3.66940i) q^{74} +(6.28788 + 1.43873i) q^{75} +(0.393163 + 2.22974i) q^{76} +(5.60091 - 4.69972i) q^{77} +(-1.79107 - 1.15816i) q^{78} +(-11.6079 + 4.22493i) q^{79} +5.61331 q^{80} +(-5.96969 + 6.73519i) q^{81} +3.01948 q^{82} +(10.9786 - 3.99588i) q^{83} +(-4.69308 - 3.03470i) q^{84} +(-1.63507 + 1.37199i) q^{85} +(1.46824 + 8.32679i) q^{86} +(8.98227 + 2.05523i) q^{87} +(2.82886 + 2.37370i) q^{88} +(2.86437 - 4.96123i) q^{89} +(-3.32998 + 4.62121i) q^{90} +(-1.43183 - 2.48001i) q^{91} +(-0.835346 + 4.73748i) q^{92} +(2.30412 - 0.287484i) q^{93} +(-2.69893 - 0.982329i) q^{94} +(2.91133 + 1.05964i) q^{95} +(2.96727 - 7.02862i) q^{96} +(-0.0596270 + 0.338162i) q^{97} +(-6.95870 - 12.0528i) q^{98} +(-5.43934 + 1.37879i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) $ 12 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 6 * q^8	\( 12 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 6 q^{8} - 3 q^{10} + 3 q^{11} + 12 q^{12} - 6 q^{13} + 15 q^{14} + 9 q^{15} + 9 q^{17} + 9 q^{18} - 3 q^{19} - 3 q^{20} - 12 q^{21} + 3 q^{22} - 12 q^{23} - 18 q^{24} + 3 q^{25} - 30 q^{26} - 9 q^{27} - 12 q^{28} - 6 q^{29} - 9 q^{30} + 3 q^{31} + 9 q^{34} + 12 q^{35} + 18 q^{36} - 3 q^{37} + 42 q^{38} + 33 q^{39} + 21 q^{40} + 15 q^{41} + 18 q^{42} + 3 q^{43} + 3 q^{44} - 9 q^{45} - 3 q^{46} - 15 q^{47} - 15 q^{48} + 12 q^{49} - 33 q^{50} - 18 q^{51} + 9 q^{52} - 18 q^{53} - 54 q^{54} - 12 q^{55} - 33 q^{56} - 3 q^{57} + 21 q^{58} - 12 q^{59} + 12 q^{61} - 12 q^{62} + 9 q^{63} + 12 q^{64} + 3 q^{65} - 9 q^{66} - 15 q^{67} + 9 q^{68} + 9 q^{69} - 15 q^{70} + 27 q^{71} + 18 q^{72} + 6 q^{73} + 33 q^{74} + 39 q^{75} - 48 q^{76} + 15 q^{77} + 18 q^{78} - 42 q^{79} + 42 q^{80} + 36 q^{81} - 12 q^{82} + 39 q^{83} + 6 q^{84} - 27 q^{85} + 51 q^{86} + 9 q^{87} - 30 q^{88} + 9 q^{89} + 18 q^{90} + 6 q^{91} - 39 q^{92} - 39 q^{93} - 15 q^{94} - 33 q^{95} + 3 q^{97} - 45 q^{98} - 27 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 6 * q^8 - 3 * q^10 + 3 * q^11 + 12 * q^12 - 6 * q^13 + 15 * q^14 + 9 * q^15 + 9 * q^17 + 9 * q^18 - 3 * q^19 - 3 * q^20 - 12 * q^21 + 3 * q^22 - 12 * q^23 - 18 * q^24 + 3 * q^25 - 30 * q^26 - 9 * q^27 - 12 * q^28 - 6 * q^29 - 9 * q^30 + 3 * q^31 + 9 * q^34 + 12 * q^35 + 18 * q^36 - 3 * q^37 + 42 * q^38 + 33 * q^39 + 21 * q^40 + 15 * q^41 + 18 * q^42 + 3 * q^43 + 3 * q^44 - 9 * q^45 - 3 * q^46 - 15 * q^47 - 15 * q^48 + 12 * q^49 - 33 * q^50 - 18 * q^51 + 9 * q^52 - 18 * q^53 - 54 * q^54 - 12 * q^55 - 33 * q^56 - 3 * q^57 + 21 * q^58 - 12 * q^59 + 12 * q^61 - 12 * q^62 + 9 * q^63 + 12 * q^64 + 3 * q^65 - 9 * q^66 - 15 * q^67 + 9 * q^68 + 9 * q^69 - 15 * q^70 + 27 * q^71 + 18 * q^72 + 6 * q^73 + 33 * q^74 + 39 * q^75 - 48 * q^76 + 15 * q^77 + 18 * q^78 - 42 * q^79 + 42 * q^80 + 36 * q^81 - 12 * q^82 + 39 * q^83 + 6 * q^84 - 27 * q^85 + 51 * q^86 + 9 * q^87 - 30 * q^88 + 9 * q^89 + 18 * q^90 + 6 * q^91 - 39 * q^92 - 39 * q^93 - 15 * q^94 - 33 * q^95 + 3 * q^97 - 45 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.57954	+	0.574906i	−1.11690	+	0.406520i	−0.833521	−	0.552487i	$-0.813679\pi$
$2$	−1.57954	+	0.574906i	−1.11690	+	0.406520i	−0.283383	+	0.959007i	$0.591457\pi$
$3$	1.45446	+	0.940501i	0.839734	+	0.542999i
$3$	1.45446	+	0.940501i	0.839734	+	0.542999i
$4$	0.632343	−	0.530599i	0.316172	−	0.265300i
$5$	−0.196143	−	1.11238i	−0.0877179	−	0.497473i	−0.996737	−	0.0807185i	$-0.974279\pi$
$5$	−0.196143	−	1.11238i	−0.0877179	−	0.497473i	0.909019	−	0.416755i	$-0.136833\pi$
$6$	−2.83808	−	0.649381i	−1.15864	−	0.265109i
$7$	−2.99441	−	2.51261i	−1.13178	−	0.949676i	−0.132641	−	0.991164i	$-0.542346\pi$
$7$	−2.99441	−	2.51261i	−1.13178	−	0.949676i	−0.999139	+	0.0414879i	$0.986790\pi$
$8$	0.987144	−	1.70978i	0.349008	−	0.604500i
$9$	1.23092	+	2.73584i	0.410305	+	0.911948i
$10$	0.949332	+	1.64429i	0.300205	+	0.519971i
$11$	−0.324801	+	1.84204i	−0.0979313	+	0.555396i	0.895878	+	0.444299i	$0.146547\pi$
$11$	−0.324801	+	1.84204i	−0.0979313	+	0.555396i	−0.993810	+	0.111096i	$0.964564\pi$
$12$	1.41875	−	0.177016i	0.409557	−	0.0511002i
$13$	0.688417	+	0.250563i	0.190932	+	0.0694937i	0.435717	−	0.900084i	$-0.356495\pi$
$13$	0.688417	+	0.250563i	0.190932	+	0.0694937i	−0.244784	+	0.969578i	$0.578717\pi$
$14$	6.17430	+	2.24726i	1.65015	+	0.600606i
$15$	0.760915	−	1.80239i	0.196467	−	0.465376i
$16$	−0.862951	+	4.89404i	−0.215738	+	1.22351i
$17$	−0.944822	−	1.63648i	−0.229153	−	0.396905i	0.728404	−	0.685147i	$-0.240262\pi$
$17$	−0.944822	−	1.63648i	−0.229153	−	0.396905i	−0.957557	+	0.288243i	$0.906929\pi$
$18$	−3.51713	−	3.61372i	−0.828997	−	0.851761i
$19$	−1.37143	+	2.37538i	−0.314627	+	0.544950i	−0.979358	−	0.202133i	$-0.935213\pi$
$19$	−1.37143	+	2.37538i	−0.314627	+	0.544950i	0.664731	+	0.747083i	$0.268546\pi$
$20$	−0.714260	−	0.599335i	−0.159713	−	0.134015i
$21$	−1.99214	−	6.47073i	−0.434721	−	1.41203i
$22$	−0.545962	−	3.09631i	−0.116400	−	0.660135i
$23$	−4.46428	+	3.74597i	−0.930866	+	0.781089i	−0.975973	−	0.217893i	$-0.930082\pi$
$23$	−4.46428	+	3.74597i	−0.930866	+	0.781089i	0.0451066	+	0.998982i	$0.485637\pi$
$24$	3.04382	−	1.55840i	0.621317	−	0.318108i
$25$	3.49954	−	1.27373i	0.699908	−	0.254746i
$26$	−1.23143			−0.241504
$27$	−0.782746	+	5.13686i	−0.150640	+	0.988589i
$28$	−3.22668			−0.609786
$29$	4.99910	−	1.81953i	0.928310	−	0.337877i	0.166771	−	0.985996i	$-0.446666\pi$
$29$	4.99910	−	1.81953i	0.928310	−	0.337877i	0.761540	+	0.648118i	$0.224444\pi$
$30$	−0.165691	+	3.28441i	−0.0302509	+	0.599648i
$31$	1.02696	−	0.861722i	0.184447	−	0.154770i	−0.545889	−	0.837858i	$-0.683808\pi$
$31$	1.02696	−	0.861722i	0.184447	−	0.154770i	0.730336	+	0.683088i	$0.239363\pi$
$32$	−0.764882	−	4.33786i	−0.135213	−	0.766833i
$33$	−2.20485	+	2.37370i	−0.383815	+	0.413208i
$34$	2.43321	+	2.04170i	0.417291	+	0.350149i
$35$	−2.20765	+	3.82376i	−0.373161	+	0.646334i
$36$	2.23000	+	1.07687i	0.371666	+	0.179478i
$37$	−1.69806	−	2.94112i	−0.279159	−	0.483517i	0.692017	−	0.721881i	$-0.256722\pi$
$37$	−1.69806	−	2.94112i	−0.279159	−	0.483517i	−0.971176	+	0.238364i	$0.923389\pi$
$38$	0.800605	−	4.54046i	0.129875	−	0.736559i
$39$	0.765621	+	1.01189i	0.122597	+	0.162032i
$40$	−2.09556	−	0.762721i	−0.331337	−	0.120597i
$41$	−1.68800	−	0.614382i	−0.263621	−	0.0959503i	0.206828	−	0.978377i	$-0.433686\pi$
$41$	−1.68800	−	0.614382i	−0.263621	−	0.0959503i	−0.470449	+	0.882427i	$0.655908\pi$
$42$	6.86673	+	9.07549i	1.05956	+	1.40038i
$43$	0.873477	−	4.95373i	0.133204	−	0.755437i	−0.842890	−	0.538087i	$-0.819147\pi$
$43$	0.873477	−	4.95373i	0.133204	−	0.755437i	0.976094	−	0.217351i	$-0.0697415\pi$
$44$	0.771999	+	1.33714i	0.116383	+	0.201582i
$45$	2.80187	−	1.90587i	0.417679	−	0.284110i
$46$	4.89793	−	8.48346i	0.722160	−	1.25082i
$47$	1.30892	+	1.09832i	0.190926	+	0.160206i	0.733240	−	0.679970i	$-0.238007\pi$
$47$	1.30892	+	1.09832i	0.190926	+	0.160206i	−0.542314	+	0.840176i	$0.682452\pi$
$48$	−5.85798	+	6.30658i	−0.845526	+	0.910277i
$49$	1.43775	+	8.15389i	0.205393	+	1.16484i
$50$	−4.79539	+	4.02381i	−0.678170	+	0.569053i
$51$	0.164904	−	3.26880i	0.0230912	−	0.457724i
$52$	0.568265	−	0.206831i	0.0788041	−	0.0286824i
$53$	2.84494			0.390783			0.195391	−	0.980725i	$-0.437402\pi$
$53$	2.84494			0.390783			0.195391	+	0.980725i	$0.437402\pi$
$54$	−1.71683	−	8.56388i	−0.233631	−	1.16540i
$55$	2.11276			0.284885
$56$	−7.25193	+	2.63949i	−0.969080	+	0.352716i
$57$	−4.22874	+	2.16507i	−0.560110	+	0.286771i
$58$	−6.85023	+	5.74803i	−0.899480	+	0.754753i
$59$	−1.95529	−	11.0890i	−0.254557	−	1.44366i	−0.797208	−	0.603704i	$-0.793691\pi$
$59$	−1.95529	−	11.0890i	−0.254557	−	1.44366i	0.542652	−	0.839958i	$-0.317420\pi$
$60$	−0.475188	−	1.54347i	−0.0613465	−	0.199261i
$61$	4.00710	+	3.36235i	0.513056	+	0.430505i	0.862203	−	0.506563i	$-0.169084\pi$
$61$	4.00710	+	3.36235i	0.513056	+	0.430505i	−0.349147	+	0.937068i	$0.613529\pi$
$62$	−1.12672	+	1.95153i	−0.143093	+	0.247844i
$63$	3.18824	−	11.2850i	0.401680	−	1.42178i
$64$	−1.26751	−	2.19540i	−0.158439	−	0.274425i
$65$	0.143694	−	0.814930i	0.0178231	−	0.101080i
$66$	2.11800	−	5.01694i	0.260708	−	0.617542i
$67$	1.77511	+	0.646086i	0.216864	+	0.0789319i	0.448167	−	0.893950i	$-0.352077\pi$
$67$	1.77511	+	0.646086i	0.216864	+	0.0789319i	−0.231304	+	0.972882i	$0.574299\pi$
$68$	−1.46577	−	0.533495i	−0.177750	−	0.0646958i
$69$	−10.0162	+	1.24972i	−1.20581	+	0.150448i
$70$	1.28877	−	7.30898i	0.154038	−	0.873590i
$71$	6.09193	+	10.5515i	0.722980	+	1.25224i	0.959800	+	0.280684i	$0.0905613\pi$
$71$	6.09193	+	10.5515i	0.722980	+	1.25224i	−0.236821	+	0.971553i	$0.576105\pi$
$72$	5.89280	+	0.596074i	0.694473	+	0.0702480i
$73$	−4.94384	+	8.56298i	−0.578633	+	1.00222i	0.417004	+	0.908905i	$0.363080\pi$
$73$	−4.94384	+	8.56298i	−0.578633	+	1.00222i	−0.995637	+	0.0933164i	$0.970253\pi$
$74$	4.37302	+	3.66940i	0.508353	+	0.426559i
$75$	6.28788	+	1.43873i	0.726062	+	0.166130i
$76$	0.393163	+	2.22974i	0.0450989	+	0.255768i
$77$	5.60091	−	4.69972i	0.638283	−	0.535583i
$78$	−1.79107	−	1.15816i	−0.202799	−	0.131136i
$79$	−11.6079	+	4.22493i	−1.30599	+	0.475342i	−0.898943	−	0.438065i	$-0.855664\pi$
$79$	−11.6079	+	4.22493i	−1.30599	+	0.475342i	−0.407048	+	0.913407i	$0.633442\pi$
$80$	5.61331			0.627587
$81$	−5.96969	+	6.73519i	−0.663299	+	0.748354i
$82$	3.01948			0.333445
$83$	10.9786	−	3.99588i	1.20506	−	0.438605i	0.340070	−	0.940400i	$-0.389549\pi$
$83$	10.9786	−	3.99588i	1.20506	−	0.438605i	0.864986	+	0.501796i	$0.167327\pi$
$84$	−4.69308	−	3.03470i	−0.512057	−	0.331113i
$85$	−1.63507	+	1.37199i	−0.177349	+	0.148813i
$86$	1.46824	+	8.32679i	0.158324	+	0.897901i
$87$	8.98227	+	2.05523i	0.963000	+	0.220344i
$88$	2.82886	+	2.37370i	0.301558	+	0.253037i
$89$	2.86437	−	4.96123i	0.303622	−	0.525889i	−0.673331	−	0.739341i	$-0.735137\pi$
$89$	2.86437	−	4.96123i	0.303622	−	0.525889i	0.976954	+	0.213452i	$0.0684706\pi$
$90$	−3.32998	+	4.62121i	−0.351011	+	0.487118i
$91$	−1.43183	−	2.48001i	−0.150097	−	0.259976i
$92$	−0.835346	+	4.73748i	−0.0870908	+	0.493917i
$93$	2.30412	−	0.287484i	0.238926	−	0.0298107i
$94$	−2.69893	−	0.982329i	−0.278373	−	0.101319i
$95$	2.91133	+	1.05964i	0.298697	+	0.108717i
$96$	2.96727	−	7.02862i	0.302846	−	0.717356i
$97$	−0.0596270	+	0.338162i	−0.00605421	+	0.0343351i	−0.987685	−	0.156454i	$-0.949994\pi$
$97$	−0.0596270	+	0.338162i	−0.00605421	+	0.0343351i	0.981631	+	0.190789i	$0.0611047\pi$
$98$	−6.95870	−	12.0528i	−0.702935	−	1.21752i
$99$	−5.43934	+	1.37879i	−0.546674	+	0.138574i
$100$	1.53707	−	2.66228i	0.153707	−	0.266228i
$101$	−13.3309	−	11.1860i	−1.32647	−	1.11304i	−0.984888	−	0.173194i	$-0.944591\pi$
$101$	−13.3309	−	11.1860i	−1.32647	−	1.11304i	−0.341586	−	0.939850i	$-0.610964\pi$
$102$	1.61878	+	5.25801i	0.160283	+	0.520621i
$103$	−2.74590	−	15.5728i	−0.270561	−	1.53443i	−0.752717	−	0.658345i	$-0.771257\pi$
$103$	−2.74590	−	15.5728i	−0.270561	−	1.53443i	0.482155	−	0.876086i	$-0.339854\pi$
$104$	1.10798	−	0.929702i	0.108646	−	0.0911648i
$105$	−6.80719	+	3.48522i	−0.664314	+	0.340122i
$106$	−4.49370	+	1.63557i	−0.436467	+	0.158861i
$107$	−16.5298			−1.59800			−0.798999	−	0.601332i	$-0.794637\pi$
$107$	−16.5298			−1.59800			−0.798999	+	0.601332i	$0.794637\pi$
$108$	2.23065	+	3.66358i	0.214644	+	0.352528i
$109$	−4.71844			−0.451945			−0.225972	−	0.974134i	$-0.572556\pi$
$109$	−4.71844			−0.451945			−0.225972	+	0.974134i	$0.572556\pi$
$110$	−3.33719	+	1.21464i	−0.318189	+	0.115811i
$111$	0.296369	−	5.87477i	0.0281301	−	0.557608i
$112$	14.8808	−	12.4865i	1.40611	−	1.17986i
$113$	3.46338	+	19.6418i	0.325807	+	1.84775i	0.503939	+	0.863739i	$0.331884\pi$
$113$	3.46338	+	19.6418i	0.325807	+	1.84775i	−0.178132	+	0.984007i	$0.557005\pi$
$114$	5.43475	−	5.85095i	0.509011	−	0.547992i
$115$	5.04260	+	4.23124i	0.470225	+	0.394565i
$116$	2.19571	−	3.80308i	0.203867	−	0.353108i
$117$	0.161881	+	2.19182i	0.0149659	+	0.202634i
$118$	9.46357	+	16.3914i	0.871193	+	1.50895i
$119$	−1.28265	+	7.27425i	−0.117580	+	0.666830i
$120$	−2.33057	−	3.08022i	−0.212751	−	0.281185i
$121$	7.04901	+	2.56563i	0.640819	+	0.233239i
$122$	−8.26241	−	3.00727i	−0.748043	−	0.272266i
$123$	−1.87730	−	2.48116i	−0.169271	−	0.223719i
$124$	0.192163	−	1.08981i	0.0172567	−	0.0978676i
$125$	−4.92714	−	8.53407i	−0.440697	−	0.763310i
$126$	1.45188	+	19.6581i	0.129344	+	1.75128i
$127$	−0.534728	+	0.926176i	−0.0474495	+	0.0821849i	−0.888775	−	0.458344i	$-0.848443\pi$
$127$	−0.534728	+	0.926176i	−0.0474495	+	0.0821849i	0.841325	+	0.540529i	$0.181776\pi$
$128$	10.0128	+	8.40170i	0.885011	+	0.742612i
$129$	5.92943	−	6.38351i	0.522057	−	0.562037i
$130$	0.241537	+	1.36983i	0.0211842	+	0.120142i
$131$	5.85281	−	4.91109i	0.511362	−	0.429084i	−0.350246	−	0.936658i	$-0.613902\pi$
$131$	5.85281	−	4.91109i	0.511362	−	0.429084i	0.861608	+	0.507574i	$0.169458\pi$
$132$	−0.134740	+	2.67089i	−0.0117276	+	0.232471i
$133$	10.0750	−	3.66701i	0.873615	−	0.317970i
$134$	−3.17529			−0.274303
$135$	5.86769	−	0.136846i	0.505010	−	0.0117778i
$136$	−3.73070			−0.319905
$137$	−14.7067	+	5.35279i	−1.25647	+	0.457319i	−0.882585	−	0.470154i	$-0.844199\pi$
$137$	−14.7067	+	5.35279i	−1.25647	+	0.457319i	−0.373890	+	0.927473i	$0.621976\pi$
$138$	15.1025	−	7.73235i	1.28561	−	0.658222i
$139$	6.63160	−	5.56457i	0.562485	−	0.471981i	−0.316658	−	0.948540i	$-0.602561\pi$
$139$	6.63160	−	5.56457i	0.562485	−	0.471981i	0.879142	+	0.476559i	$0.158116\pi$
$140$	0.632892	+	3.58931i	0.0534891	+	0.303352i
$141$	0.870810	+	2.82850i	0.0733354	+	0.238203i
$142$	−15.6886	−	13.1643i	−1.31656	−	1.10472i
$143$	−0.685146	+	1.18671i	−0.0572948	+	0.0992375i
$144$	−14.4516	+	3.66325i	−1.20430	+	0.305271i
$145$	−3.00455	−	5.20403i	−0.249514	−	0.432172i
$146$	2.88609	−	16.3678i	0.238854	−	1.35461i
$147$	−5.57759	+	13.2117i	−0.460032	+	1.08968i
$148$	−2.63431	−	0.958811i	−0.216539	−	0.0788137i
$149$	2.31524	+	0.842677i	0.189672	+	0.0690348i	0.435110	−	0.900377i	$-0.356710\pi$
$149$	2.31524	+	0.842677i	0.189672	+	0.0690348i	−0.245438	+	0.969412i	$0.578932\pi$
$150$	−10.7591	+	1.34241i	−0.878477	+	0.109607i
$151$	−1.82563	+	10.3537i	−0.148568	+	0.842571i	0.815865	+	0.578243i	$0.196261\pi$
$151$	−1.82563	+	10.3537i	−0.148568	+	0.842571i	−0.964433	+	0.264328i	$0.914850\pi$
$152$	2.70760	+	4.68969i	0.219615	+	0.380384i
$153$	3.31416	−	4.59925i	0.267934	−	0.371828i
$154$	−6.14497	+	10.6434i	−0.495176	+	0.857669i
$155$	−1.16000	−	0.973353i	−0.0931731	−	0.0781816i
$156$	1.02104	+	0.233625i	0.0817489	+	0.0187050i
$157$	0.0625044	+	0.354480i	0.00498840	+	0.0282906i	0.987200	−	0.159485i	$-0.0509833\pi$
$157$	0.0625044	+	0.354480i	0.00498840	+	0.0282906i	−0.982212	+	0.187776i	$0.939872\pi$
$158$	15.9062	−	13.3469i	1.26543	−	1.06182i
$159$	4.13786	+	2.67567i	0.328154	+	0.212195i
$160$	−4.67534	+	1.70168i	−0.369618	+	0.134530i
$161$	22.7800			1.79532
$162$	5.55728	−	14.0705i	0.436621	−	1.10548i
$163$	14.6186			1.14502			0.572508	−	0.819899i	$-0.305971\pi$
$163$	14.6186			1.14502			0.572508	+	0.819899i	$0.305971\pi$
$164$	−1.39339	+	0.507151i	−0.108805	+	0.0396019i
$165$	3.07293	+	1.98706i	0.239227	+	0.154692i
$166$	−15.0439	+	12.6233i	−1.16763	+	0.979758i
$167$	0.377832	+	2.14279i	0.0292375	+	0.165814i	0.995930	−	0.0901247i	$-0.0287265\pi$
$167$	0.377832	+	2.14279i	0.0292375	+	0.165814i	−0.966693	+	0.255939i	$0.917615\pi$
$168$	−13.0301	−	2.98142i	−1.00529	−	0.230021i
$169$	−9.54744	−	8.01125i	−0.734419	−	0.616250i
$170$	1.79390	−	3.10712i	0.137586	−	0.238306i
$171$	−8.18679	−	0.828119i	−0.626060	−	0.0633278i
$172$	−2.07611	−	3.59593i	−0.158302	−	0.274187i
$173$	−3.05048	+	17.3001i	−0.231924	+	1.31531i	0.617072	+	0.786906i	$0.288319\pi$
$173$	−3.05048	+	17.3001i	−0.231924	+	1.31531i	−0.848996	+	0.528399i	$0.822793\pi$
$174$	−15.3694	+	1.91763i	−1.16515	+	0.145375i
$175$	−13.6794	−	4.97890i	−1.03407	−	0.376370i
$176$	−8.73473	−	3.17918i	−0.658405	−	0.239640i
$177$	7.58531	−	17.9674i	0.570147	−	1.35052i
$178$	−1.67214	+	9.48320i	−0.125333	+	0.710796i
$179$	−0.502236	−	0.869898i	−0.0375388	−	0.0650192i	0.846646	−	0.532157i	$-0.178618\pi$
$179$	−0.502236	−	0.869898i	−0.0375388	−	0.0650192i	−0.884184	+	0.467138i	$0.845285\pi$
$180$	0.760494	−	2.69183i	0.0566839	−	0.200638i
$181$	10.5866	−	18.3366i	0.786898	−	1.36295i	−0.140961	−	0.990015i	$-0.545019\pi$
$181$	10.5866	−	18.3366i	0.786898	−	1.36295i	0.927859	−	0.372932i	$-0.121647\pi$
$182$	3.68741	+	3.09411i	0.273329	+	0.229350i
$183$	2.66587	+	8.65909i	0.197067	+	0.640099i
$184$	1.99792	+	11.3308i	0.147289	+	0.835315i
$185$	−2.93859	+	2.46577i	−0.216050	+	0.181287i
$186$	−3.47418	+	1.77875i	−0.254739	+	0.130424i
$187$	3.32134	−	1.20887i	0.242880	−	0.0884012i
$188$	1.41045			0.102868
$189$	15.2508	−	13.4151i	1.10933	−	0.975806i
$190$	−5.20776			−0.377811
$191$	9.23566	−	3.36150i	0.668269	−	0.243230i	0.0144664	−	0.999895i	$-0.495395\pi$
$191$	9.23566	−	3.36150i	0.668269	−	0.243230i	0.653802	+	0.756665i	$0.273173\pi$
$192$	0.221225	−	4.38522i	0.0159655	−	0.316476i
$193$	−8.54606	+	7.17099i	−0.615159	+	0.516179i	−0.896278	−	0.443494i	$-0.853739\pi$
$193$	−8.54606	+	7.17099i	−0.615159	+	0.516179i	0.281119	+	0.959673i	$0.409294\pi$
$194$	−0.100228	−	0.568420i	−0.00719594	−	0.0408102i
$195$	0.975440	−	1.05014i	0.0698527	−	0.0752021i
$196$	5.23560	+	4.39319i	0.373971	+	0.313799i
$197$	−4.54497	+	7.87212i	−0.323816	+	0.560865i	−0.981272	−	0.192628i	$-0.938299\pi$
$197$	−4.54497	+	7.87212i	−0.323816	+	0.560865i	0.657456	+	0.753493i	$0.271632\pi$
$198$	7.79898	−	5.30496i	0.554249	−	0.377007i
$199$	7.34694	+	12.7253i	0.520811	+	0.902071i	0.999707	+	0.0241994i	$0.00770367\pi$
$199$	7.34694	+	12.7253i	0.520811	+	0.902071i	−0.478896	+	0.877872i	$0.658963\pi$
$200$	1.27675	−	7.24081i	0.0902798	−	0.512002i
$201$	1.97418	+	2.60920i	0.139248	+	0.184038i
$202$	27.4876	+	10.0047i	1.93402	+	0.703925i
$203$	−19.5411	−	7.11238i	−1.37152	−	0.499191i
$204$	−1.63015	−	2.15450i	−0.114133	−	0.150845i
$205$	−0.352339	+	1.99821i	−0.0246084	+	0.139561i
$206$	13.2901	+	23.0192i	0.925968	+	1.60382i
$207$	−15.7435	−	7.60259i	−1.09425	−	0.528417i
$208$	−1.82034	+	3.15292i	−0.126218	+	0.218615i
$209$	−3.93011	−	3.29775i	−0.271851	−	0.228110i
$210$	8.74857	−	9.41854i	0.603709	−	0.649941i
$211$	1.36458	+	7.73891i	0.0939415	+	0.532769i	0.995067	+	0.0992096i	$0.0316314\pi$
$211$	1.36458	+	7.73891i	0.0939415	+	0.532769i	−0.901125	+	0.433559i	$0.857257\pi$
$212$	1.79898	−	1.50952i	0.123555	−	0.103675i
$213$	−1.06325	+	21.0763i	−0.0728528	+	1.44412i
$214$	26.1095	−	9.50309i	1.78481	−	0.649618i
$215$	−5.68178			−0.387494
$216$	8.01024	+	6.40915i	0.545028	+	0.436087i
$217$	−5.24030			−0.355735
$218$	7.45297	−	2.71266i	0.504779	−	0.183724i
$219$	−15.2441	+	7.80484i	−1.03010	+	0.527402i
$220$	1.33599	−	1.12103i	0.0900725	−	0.0755798i
$221$	−0.240390	−	1.36332i	−0.0161704	−	0.0917067i
$222$	2.90931	+	9.44982i	0.195260	+	0.634231i
$223$	−6.69591	−	5.61853i	−0.448391	−	0.376245i	0.390447	−	0.920625i	$-0.372320\pi$
$223$	−6.69591	−	5.61853i	−0.448391	−	0.376245i	−0.838838	+	0.544380i	$0.816765\pi$
$224$	−8.60897	+	14.9112i	−0.575211	+	0.996295i
$225$	7.79236	+	8.00634i	0.519490	+	0.533756i
$226$	−16.7627	−	29.0339i	−1.11504	−	1.93131i
$227$	0.706473	−	4.00661i	0.0468903	−	0.265928i	−0.952345	−	0.305022i	$-0.901336\pi$
$227$	0.706473	−	4.00661i	0.0468903	−	0.265928i	0.999236	+	0.0390942i	$0.0124473\pi$
$228$	−1.52523	+	3.61284i	−0.101011	+	0.239266i
$229$	−15.1816	−	5.52563i	−1.00323	−	0.365144i	−0.212398	−	0.977183i	$-0.568127\pi$
$229$	−15.1816	−	5.52563i	−1.00323	−	0.365144i	−0.790827	+	0.612039i	$0.790349\pi$
$230$	−10.3976	−	3.78440i	−0.685594	−	0.249536i
$231$	12.5664	−	1.56790i	0.826808	−	0.103160i
$232$	1.82384	−	10.3435i	0.119741	−	0.679086i
$233$	−8.60658	−	14.9070i	−0.563836	−	0.976592i	−0.997157	−	0.0753527i	$-0.975992\pi$
$233$	−8.60658	−	14.9070i	−0.563836	−	0.976592i	0.433321	−	0.901240i	$-0.357342\pi$
$234$	−1.51579	−	3.36901i	−0.0990903	−	0.220239i
$235$	0.965013	−	1.67145i	0.0629505	−	0.109034i
$236$	−7.12022	−	5.97457i	−0.463487	−	0.388911i
$237$	−20.8568	−	4.77225i	−1.35479	−	0.309991i
$238$	−2.15602	−	12.2274i	−0.139754	−	0.792583i
$239$	−1.17621	+	0.986962i	−0.0760830	+	0.0638412i	−0.680036	−	0.733179i	$-0.738036\pi$
$239$	−1.17621	+	0.986962i	−0.0760830	+	0.0638412i	0.603953	+	0.797020i	$0.293591\pi$
$240$	8.16435	+	5.27933i	0.527006	+	0.340779i
$241$	5.18868	−	1.88852i	0.334232	−	0.121650i	−0.169452	−	0.985538i	$-0.554200\pi$
$241$	5.18868	−	1.88852i	0.334232	−	0.121650i	0.503684	+	0.863888i	$0.331978\pi$
$242$	−12.6092			−0.810549
$243$	−15.0171	+	4.18157i	−0.963350	+	0.268248i
$244$	4.31792			0.276427
$245$	8.78825	−	3.19866i	0.561461	−	0.204355i
$246$	4.39171	+	2.83982i	0.280005	+	0.181060i
$247$	−1.53930	+	1.29162i	−0.0979432	+	0.0821841i
$248$	−0.459600	−	2.60652i	−0.0291847	−	0.165514i
$249$	19.7261	+	4.51352i	1.25009	+	0.286033i
$250$	12.6889	+	10.6473i	0.802517	+	0.673392i
$251$	10.7204	−	18.5683i	0.676668	−	1.17202i	−0.299310	−	0.954156i	$-0.596756\pi$
$251$	10.7204	−	18.5683i	0.676668	−	1.17202i	0.975978	−	0.217868i	$-0.0699102\pi$
$252$	−3.97177	−	8.82770i	−0.250198	−	0.556093i
$253$	−5.45023	−	9.44007i	−0.342653	−	0.593492i
$254$	0.312161	−	1.77035i	0.0195867	−	0.111082i
$255$	−3.66851	+	0.457717i	−0.229731	+	0.0286634i
$256$	−15.8814	−	5.78037i	−0.992590	−	0.361273i
$257$	13.8947	+	5.05727i	0.866730	+	0.315464i	0.736842	−	0.676065i	$-0.236316\pi$
$257$	13.8947	+	5.05727i	0.866730	+	0.315464i	0.129888	+	0.991529i	$0.458538\pi$
$258$	−5.69586	+	13.4919i	−0.354609	+	0.839967i
$259$	−2.30520	+	13.0735i	−0.143238	+	0.812346i
$260$	−0.341537	−	0.591560i	−0.0211812	−	0.0366870i
$261$	11.1314	+	11.4371i	0.689017	+	0.707938i
$262$	−6.42133	+	11.1221i	−0.396711	+	0.687124i
$263$	2.14704	+	1.80158i	0.132392	+	0.111090i	0.706579	−	0.707634i	$-0.250237\pi$
$263$	2.14704	+	1.80158i	0.132392	+	0.111090i	−0.574187	+	0.818724i	$0.694682\pi$
$264$	1.88201	+	6.11300i	0.115830	+	0.376229i
$265$	−0.558016	−	3.16467i	−0.0342787	−	0.194404i
$266$	−13.8057	+	11.5844i	−0.846483	+	0.710284i
$267$	8.83215	−	4.52197i	0.540519	−	0.276740i
$268$	1.46529	−	0.533322i	0.0895068	−	0.0325778i
$269$	−0.356528			−0.0217379			−0.0108689	−	0.999941i	$-0.503460\pi$
$269$	−0.356528			−0.0217379			−0.0108689	+	0.999941i	$0.503460\pi$
$270$	−9.18958	+	3.58952i	−0.559260	+	0.218451i
$271$	−12.1467			−0.737857			−0.368928	−	0.929458i	$-0.620275\pi$
$271$	−12.1467			−0.737857			−0.368928	+	0.929458i	$0.620275\pi$
$272$	8.82433	−	3.21179i	0.535054	−	0.194744i
$273$	0.249904	−	4.95372i	0.0151249	−	0.299813i
$274$	20.1524	−	16.9099i	1.21745	−	1.02156i
$275$	1.20960	+	6.85999i	0.0729418	+	0.413673i
$276$	−5.67059	+	6.10484i	−0.341329	+	0.367468i
$277$	19.1434	+	16.0632i	1.15022	+	0.965146i	0.999725	−	0.0234648i	$-0.00746978\pi$
$277$	19.1434	+	16.0632i	1.15022	+	0.965146i	0.150492	+	0.988611i	$0.451914\pi$
$278$	−7.27577	+	12.6020i	−0.436372	+	0.755818i
$279$	3.62164	+	1.74890i	0.216822	+	0.104704i
$280$	4.35854	+	7.54921i	0.260473	+	0.451152i
$281$	1.27160	−	7.21162i	0.0758575	−	0.430209i	−0.923100	−	0.384560i	$-0.874353\pi$
$281$	1.27160	−	7.21162i	0.0758575	−	0.430209i	0.998958	−	0.0456492i	$-0.0145356\pi$
$282$	−3.00160	−	3.96710i	−0.178743	−	0.236237i
$283$	13.5204	+	4.92102i	0.803703	+	0.292524i	0.711020	−	0.703172i	$-0.248233\pi$
$283$	13.5204	+	4.92102i	0.803703	+	0.292524i	0.0926830	+	0.995696i	$0.470456\pi$
$284$	9.45083	+	3.43982i	0.560804	+	0.204116i
$285$	3.23783	+	4.27932i	0.191793	+	0.253485i
$286$	0.399971	−	2.26835i	0.0236508	−	0.134130i
$287$	3.51086	+	6.08099i	0.207240	+	0.358950i
$288$	10.9262	−	7.43214i	0.643833	−	0.437943i
$289$	6.71462	−	11.6301i	0.394978	−	0.684122i
$290$	7.73764	+	6.49265i	0.454370	+	0.381262i
$291$	−0.404767	+	0.435764i	−0.0237278	+	0.0255449i
$292$	1.41731	+	8.03794i	0.0829416	+	0.470385i
$293$	−11.0429	+	9.26611i	−0.645134	+	0.541332i	−0.905590	−	0.424154i	$-0.860572\pi$
$293$	−11.0429	+	9.26611i	−0.645134	+	0.541332i	0.260456	+	0.965486i	$0.416127\pi$
$294$	1.21453	−	24.0750i	0.0708330	−	1.40409i
$295$	−11.9517	+	4.35006i	−0.695854	+	0.253270i
$296$	−6.70491			−0.389715
$297$	−9.20806	−	3.11031i	−0.534306	−	0.180478i
$298$	−4.14147			−0.239909
$299$	−4.01189	+	1.46021i	−0.232013	+	0.0844460i
$300$	4.73949	−	2.42657i	0.273635	−	0.140098i
$301$	−15.0623	+	12.6388i	−0.868178	+	0.728488i
$302$	−3.06873	−	17.4036i	−0.176586	−	1.00147i
$303$	−8.86888	−	28.8073i	−0.509504	−	1.65493i
$304$	−10.4417	−	8.76166i	−0.598875	−	0.502516i
$305$	2.95426	−	5.11693i	0.169161	−	0.292995i
$306$	−2.59071	+	9.17004i	−0.148101	+	0.524216i
$307$	15.2163	+	26.3554i	0.868440	+	1.50418i	0.863591	+	0.504193i	$0.168210\pi$
$307$	15.2163	+	26.3554i	0.868440	+	1.50418i	0.00484869	+	0.999988i	$0.498457\pi$
$308$	1.04803	−	5.94367i	0.0597171	−	0.338672i
$309$	10.6524	−	25.2325i	0.605994	−	1.43543i
$310$	2.39185	+	0.870561i	0.135848	+	0.0494446i
$311$	13.1516	+	4.78678i	0.745757	+	0.271433i	0.686819	−	0.726828i	$-0.259006\pi$
$311$	13.1516	+	4.78678i	0.745757	+	0.271433i	0.0589378	+	0.998262i	$0.481229\pi$
$312$	2.48589	−	0.310163i	0.140736	−	0.0175595i
$313$	3.83547	−	21.7520i	0.216793	−	1.22950i	−0.660974	−	0.750409i	$-0.729857\pi$
$313$	3.83547	−	21.7520i	0.216793	−	1.22950i	0.877767	−	0.479087i	$-0.159032\pi$
$314$	−0.302521	−	0.523982i	−0.0170722	−	0.0295700i
$315$	−13.1787	−	1.33306i	−0.742533	−	0.0751094i
$316$	−5.09844	+	8.83075i	−0.286810	+	0.496769i
$317$	13.3205	+	11.1773i	0.748156	+	0.627777i	0.935014	−	0.354610i	$-0.115386\pi$
$317$	13.3205	+	11.1773i	0.748156	+	0.627777i	−0.186859	+	0.982387i	$0.559831\pi$
$318$	−8.07418	−	1.84745i	−0.452777	−	0.103600i
$319$	1.72792	+	9.79953i	0.0967450	+	0.548668i
$320$	−2.19351	+	1.84058i	−0.122621	+	0.102891i
$321$	−24.0420	−	15.5463i	−1.34189	−	0.867711i
$322$	−35.9820	+	13.0964i	−2.00520	+	0.729832i
$323$	5.18302			0.288391
$324$	−0.201212	+	7.42647i	−0.0111784	+	0.412581i
$325$	2.72829			0.151338
$326$	−23.0906	+	8.40430i	−1.27887	+	0.465471i
$327$	−6.86279	−	4.43770i	−0.379513	−	0.245405i
$328$	−2.71676	+	2.27963i	−0.150008	+	0.125872i
$329$	−1.15981	−	6.57762i	−0.0639425	−	0.362636i
$330$	−5.99619	−	1.37199i	−0.330079	−	0.0755255i
$331$	0.661975	+	0.555463i	0.0363855	+	0.0305310i	0.660799	−	0.750563i	$-0.270218\pi$
$331$	0.661975	+	0.555463i	0.0363855	+	0.0305310i	−0.624414	+	0.781094i	$0.714662\pi$
$332$	4.82203	−	8.35199i	0.264643	−	0.458375i
$333$	5.95628	−	8.26589i	0.326402	−	0.452968i
$334$	−1.82870	−	3.16741i	−0.100062	−	0.173313i
$335$	0.370520	−	2.10132i	0.0202437	−	0.114808i
$336$	33.3871	−	4.16569i	1.82142	−	0.227257i
$337$	−0.393289	−	0.143145i	−0.0214238	−	0.00779762i	0.331286	−	0.943530i	$-0.392517\pi$
$337$	−0.393289	−	0.143145i	−0.0214238	−	0.00779762i	−0.352710	+	0.935733i	$0.614740\pi$
$338$	19.6863	+	7.16522i	1.07079	+	0.389737i
$339$	−13.4358	+	31.8256i	−0.729732	+	1.72853i
$340$	−0.305951	+	1.73514i	−0.0165925	+	0.0941010i
$341$	1.25377	+	2.17159i	0.0678953	+	0.117598i
$342$	13.4075	−	3.39859i	0.724992	−	0.183775i
$343$	2.50108	−	4.33199i	0.135046	−	0.233906i
$344$	−7.60757	−	6.38351i	−0.410173	−	0.344176i
$345$	3.35478	+	10.8967i	0.180615	+	0.586661i
$346$	−5.12759	−	29.0800i	−0.275661	−	1.56335i
$347$	17.9329	−	15.0475i	0.962689	−	0.807792i	−0.0186996	−	0.999825i	$-0.505953\pi$
$347$	17.9329	−	15.0475i	0.962689	−	0.807792i	0.981388	+	0.192033i	$0.0615082\pi$
$348$	6.77038	−	3.46637i	0.362931	−	0.185817i
$349$	−19.8993	+	7.24276i	−1.06519	+	0.387696i	−0.814374	−	0.580340i	$-0.802920\pi$
$349$	−19.8993	+	7.24276i	−1.06519	+	0.387696i	−0.250811	+	0.968036i	$0.580697\pi$
$350$	24.4696			1.30796
$351$	−1.82596	+	3.34017i	−0.0974627	+	0.178285i
$352$	8.23894			0.439137
$353$	−22.1246	+	8.05268i	−1.17757	+	0.428601i	−0.855344	−	0.518061i	$-0.826654\pi$
$353$	−22.1246	+	8.05268i	−1.17757	+	0.428601i	−0.322228	+	0.946662i	$0.604432\pi$
$354$	−1.65172	+	32.7411i	−0.0877878	+	1.74017i
$355$	10.5425	−	8.84618i	0.559536	−	0.469507i
$356$	−0.821160	−	4.65703i	−0.0435214	−	0.246822i
$357$	−8.70700	+	9.37379i	−0.460823	+	0.496114i
$358$	1.29341	+	1.08530i	0.0683589	+	0.0573599i
$359$	5.23047	−	9.05943i	0.276053	−	0.478139i	−0.694347	−	0.719640i	$-0.744307\pi$
$359$	5.23047	−	9.05943i	0.276053	−	0.478139i	0.970400	+	0.241502i	$0.0776400\pi$
$360$	−0.492769	−	6.67197i	−0.0259712	−	0.351644i
$361$	5.73837	+	9.93915i	0.302019	+	0.523113i
$362$	−6.18020	+	35.0497i	−0.324824	+	1.84217i
$363$	7.83953	+	10.3612i	0.411469	+	0.543822i
$364$	−2.22130	−	0.808488i	−0.116428	−	0.0423763i
$365$	10.4950	+	3.81988i	0.549335	+	0.199941i
$366$	−9.18901	−	12.1448i	−0.480317	−	0.634817i
$367$	3.69146	−	20.9353i	0.192693	−	1.09281i	−0.722974	−	0.690875i	$-0.757225\pi$
$367$	3.69146	−	20.9353i	0.192693	−	1.09281i	0.915666	−	0.401939i	$-0.131664\pi$
$368$	−14.4805	−	25.0809i	−0.754848	−	1.30743i
$369$	−0.396932	−	5.37436i	−0.0206635	−	0.279778i
$370$	3.22404	−	5.58420i	0.167610	−	0.290309i
$371$	−8.51892	−	7.14822i	−0.442280	−	0.371117i
$372$	1.30446	−	1.40435i	0.0676330	−	0.0728124i
$373$	0.401142	+	2.27499i	0.0207704	+	0.117795i	0.993430	−	0.114440i	$-0.0365074\pi$
$373$	0.401142	+	2.27499i	0.0207704	+	0.117795i	−0.972660	+	0.232235i	$0.925396\pi$
$374$	−4.55120	+	3.81891i	−0.235337	+	0.197471i
$375$	0.859956	−	17.0465i	0.0444079	−	0.880275i
$376$	3.16998	−	1.15378i	0.163479	−	0.0595016i
$377$	3.89737			0.200725
$378$	−16.3768	+	29.9575i	−0.842331	+	1.54085i
$379$	12.5539			0.644850			0.322425	−	0.946595i	$-0.395502\pi$
$379$	12.5539			0.644850			0.322425	+	0.946595i	$0.395502\pi$
$380$	2.40321	−	0.874696i	0.123282	−	0.0448709i
$381$	−1.64881	+	0.844175i	−0.0844712	+	0.0432484i
$382$	−12.6555	+	10.6193i	−0.647514	+	0.543329i
$383$	−3.41297	−	19.3559i	−0.174395	−	0.989042i	−0.938840	−	0.344353i	$-0.888098\pi$
$383$	−3.41297	−	19.3559i	−0.174395	−	0.989042i	0.764445	−	0.644689i	$-0.223013\pi$
$384$	6.66136	+	21.6369i	0.339936	+	1.10416i
$385$	−6.32647	−	5.30854i	−0.322427	−	0.270548i
$386$	9.37620	−	16.2401i	0.477236	−	0.826597i
$387$	14.6278	−	3.70793i	0.743574	−	0.188485i
$388$	0.141724	+	0.245472i	0.00719492	+	0.0124620i
$389$	−3.27198	+	18.5563i	−0.165896	+	0.940843i	0.782240	+	0.622978i	$0.214077\pi$
$389$	−3.27198	+	18.5563i	−0.165896	+	0.940843i	−0.948136	+	0.317866i	$0.897034\pi$
$390$	−0.937016	+	2.21952i	−0.0474477	+	0.112390i
$391$	10.3482	+	3.76642i	0.523329	+	0.190476i
$392$	15.3607	+	5.59082i	0.775831	+	0.282379i
$393$	13.1316	−	1.63842i	0.662400	−	0.0826472i
$394$	2.65324	−	15.0473i	0.133668	−	0.758070i
$395$	6.97656	+	12.0838i	0.351029	+	0.608000i
$396$	−2.70794	+	3.75798i	−0.136079	+	0.188845i
$397$	−10.0589	+	17.4225i	−0.504841	+	0.874410i	0.495143	+	0.868811i	$0.335116\pi$
$397$	−10.0589	+	17.4225i	−0.504841	+	0.874410i	−0.999984	+	0.00559897i	$0.998218\pi$
$398$	−18.9206	−	15.8763i	−0.948405	−	0.795807i
$399$	18.1026	+	4.14205i	0.906261	+	0.207362i
$400$	3.21374	+	18.2260i	0.160687	+	0.911302i
$401$	−23.5985	+	19.8015i	−1.17845	+	0.988840i	−0.178466	+	0.983946i	$0.557113\pi$
$401$	−23.5985	+	19.8015i	−1.17845	+	0.988840i	−0.999988	+	0.00489430i	$0.998442\pi$
$402$	−4.61834	−	2.98636i	−0.230342	−	0.148946i
$403$	0.922892	−	0.335905i	0.0459725	−	0.0167326i
$404$	−14.3650			−0.714684
$405$	8.66303	+	5.31953i	0.430469	+	0.264330i
$406$	34.9549			1.73478
$407$	5.96919	−	2.17261i	0.295882	−	0.107692i
$408$	−5.42616	−	3.50873i	−0.268635	−	0.173708i
$409$	30.4059	−	25.5136i	1.50347	−	1.26156i	0.628086	−	0.778144i	$-0.283839\pi$
$409$	30.4059	−	25.5136i	1.50347	−	1.26156i	0.875388	−	0.483421i	$-0.160606\pi$
$410$	−0.592250	−	3.35882i	−0.0292491	−	0.165880i
$411$	−26.4246	−	6.04621i	−1.30343	−	0.298237i
$412$	−9.99925	−	8.39037i	−0.492628	−	0.413364i
$413$	−22.0073	+	38.1178i	−1.08291	+	1.87565i
$414$	29.2384	+	2.95755i	1.43699	+	0.145355i
$415$	−6.59832	−	11.4286i	−0.323899	−	0.561010i
$416$	0.560351	−	3.17791i	0.0274735	−	0.155810i
$417$	14.8789	−	1.85643i	0.728622	−	0.0909097i
$418$	8.10366	+	2.94949i	0.396363	+	0.144264i
$419$	−14.5099	−	5.28118i	−0.708856	−	0.258002i	−0.0376687	−	0.999290i	$-0.511993\pi$
$419$	−14.5099	−	5.28118i	−0.708856	−	0.258002i	−0.671187	+	0.741288i	$0.734215\pi$
$420$	−2.45523	+	5.81575i	−0.119803	+	0.283779i
$421$	−3.14193	+	17.8188i	−0.153128	+	0.868433i	0.807349	+	0.590074i	$0.200902\pi$
$421$	−3.14193	+	17.8188i	−0.153128	+	0.868433i	−0.960477	+	0.278359i	$0.910210\pi$
$422$	−6.60456	−	11.4394i	−0.321505	−	0.556863i
$423$	−1.39365	+	4.93294i	−0.0677616	+	0.239848i
$424$	2.80837	−	4.86424i	0.136386	−	0.236228i
$425$	−5.39087	−	4.52348i	−0.261496	−	0.219421i
$426$	−10.4374	−	33.9021i	−0.505695	−	1.64256i
$427$	−3.55061	−	20.1365i	−0.171826	−	0.974475i
$428$	−10.4525	+	8.77071i	−0.505242	+	0.423948i
$429$	−2.11262	+	1.08164i	−0.101998	+	0.0522221i
$430$	8.97460	−	3.26649i	0.432794	−	0.157524i
$431$	−28.9683			−1.39535			−0.697677	−	0.716412i	$-0.745783\pi$
$431$	−28.9683			−1.39535			−0.697677	+	0.716412i	$0.745783\pi$
$432$	−24.4645	−	8.26365i	−1.17705	−	0.397585i
$433$	−37.5902			−1.80647			−0.903235	−	0.429146i	$-0.858815\pi$
$433$	−37.5902			−1.80647			−0.903235	+	0.429146i	$0.858815\pi$
$434$	8.27727	−	3.01268i	0.397322	−	0.144613i
$435$	0.524397	−	10.3949i	0.0251429	−	0.498395i
$436$	−2.98367	+	2.50360i	−0.142892	+	0.119901i
$437$	−2.77569	−	15.7417i	−0.132779	−	0.753028i
$438$	19.5917	−	21.0920i	0.936126	−	1.00781i
$439$	7.86232	+	6.59727i	0.375248	+	0.314871i	0.810834	−	0.585277i	$-0.199014\pi$
$439$	7.86232	+	6.59727i	0.375248	+	0.314871i	−0.435585	+	0.900147i	$0.643459\pi$
$440$	2.08560	−	3.61237i	0.0994272	−	0.172213i
$441$	−20.5380	+	13.9702i	−0.978001	+	0.665248i
$442$	1.16348	+	2.01521i	0.0553413	+	0.0958540i
$443$	3.80437	−	21.5757i	0.180751	−	1.02509i	−0.750543	−	0.660822i	$-0.770208\pi$
$443$	3.80437	−	21.5757i	0.180751	−	1.02509i	0.931294	−	0.364269i	$-0.118681\pi$
$444$	−2.92974	−	3.87212i	−0.139039	−	0.183763i
$445$	−6.08062	−	2.21316i	−0.288249	−	0.104914i
$446$	13.8066	+	5.02519i	0.653761	+	0.237949i
$447$	2.57488	+	3.40312i	0.121788	+	0.160962i
$448$	−1.72072	+	9.75869i	−0.0812964	+	0.461055i
$449$	−4.98565	−	8.63540i	−0.235287	−	0.407530i	0.724069	−	0.689728i	$-0.242270\pi$
$449$	−4.98565	−	8.63540i	−0.235287	−	0.407530i	−0.959356	+	0.282198i	$0.908936\pi$
$450$	−16.9112	−	8.16647i	−0.797203	−	0.384971i
$451$	1.67998	−	2.90981i	0.0791072	−	0.137018i
$452$	12.6120	+	10.5827i	0.593217	+	0.497768i
$453$	−12.3930	+	13.3420i	−0.582272	+	0.626863i
$454$	1.18752	+	6.73475i	0.0557330	+	0.316078i
$455$	−2.47788	+	2.07919i	−0.116165	+	0.0974738i
$456$	−0.472568	+	9.36747i	−0.0221300	+	0.438672i
$457$	7.15867	−	2.60554i	0.334869	−	0.121882i	−0.169113	−	0.985597i	$-0.554090\pi$
$457$	7.15867	−	2.60554i	0.334869	−	0.121882i	0.503981	+	0.863715i	$0.331868\pi$
$458$	27.1566			1.26894
$459$	9.14592	−	3.57247i	0.426895	−	0.166748i
$460$	5.43375			0.253350
$461$	21.4255	−	7.79824i	0.997885	−	0.363200i	0.209116	−	0.977891i	$-0.432941\pi$
$461$	21.4255	−	7.79824i	0.997885	−	0.363200i	0.788768	+	0.614690i	$0.210719\pi$
$462$	−18.9477	+	9.70106i	−0.881529	+	0.451334i
$463$	−6.73792	+	5.65379i	−0.313138	+	0.262754i	−0.785787	−	0.618497i	$-0.787742\pi$
$463$	−6.73792	+	5.65379i	−0.313138	+	0.262754i	0.472650	+	0.881250i	$0.343298\pi$
$464$	4.59084	+	26.0360i	0.213125	+	1.20869i
$465$	−0.771731	−	2.50668i	−0.0357882	−	0.116245i
$466$	22.1646	+	18.5983i	1.02675	+	0.861549i
$467$	5.49878	−	9.52416i	0.254453	−	0.440726i	−0.710294	−	0.703905i	$-0.751438\pi$
$467$	5.49878	−	9.52416i	0.254453	−	0.440726i	0.964747	+	0.263180i	$0.0847713\pi$
$468$	1.26534	+	1.30009i	0.0584906	+	0.0600968i
$469$	−3.69203	−	6.39479i	−0.170482	−	0.295284i
$470$	−0.563350	+	3.19492i	−0.0259854	+	0.147371i
$471$	−0.242479	+	0.574363i	−0.0111728	+	0.0264653i
$472$	−20.8899	−	7.60331i	−0.961536	−	0.349971i
$473$	8.84127	+	3.21796i	0.406522	+	0.147962i
$474$	35.6878	−	4.45274i	1.63919	−	0.204521i
$475$	−1.77377	+	10.0596i	−0.0813863	+	0.461565i
$476$	3.04864	+	5.28040i	0.139734	+	0.242027i
$477$	3.50188	+	7.78332i	0.160340	+	0.356374i
$478$	1.29047	−	2.23516i	0.0590247	−	0.102234i
$479$	19.6816	+	16.5148i	0.899276	+	0.754582i	0.970049	−	0.242911i	$-0.0781021\pi$
$479$	19.6816	+	16.5148i	0.899276	+	0.754582i	−0.0707730	+	0.997492i	$0.522547\pi$
$480$	−8.40054	−	1.92213i	−0.383430	−	0.0877327i
$481$	−0.432034	−	2.45019i	−0.0196991	−	0.111719i
$482$	−7.11000	+	5.96600i	−0.323852	+	0.271744i
$483$	33.1327	+	21.4246i	1.50759	+	0.974855i
$484$	5.81871	−	2.11784i	0.264487	−	0.0962654i
$485$	0.387861			0.0176119
$486$	21.3162	−	15.2384i	0.966921	−	0.691228i
$487$	−30.3800			−1.37665			−0.688325	−	0.725402i	$-0.741654\pi$
$487$	−30.3800			−1.37665			−0.688325	+	0.725402i	$0.741654\pi$
$488$	9.70448	−	3.53214i	0.439301	−	0.159893i
$489$	21.2621	+	13.7488i	0.961508	+	0.621742i
$490$	−12.0425	+	10.1048i	−0.544023	+	0.456490i
$491$	1.51218	+	8.57597i	0.0682435	+	0.387028i	0.999730	+	0.0232514i	$0.00740183\pi$
$491$	1.51218	+	8.57597i	0.0682435	+	0.387028i	−0.931486	+	0.363777i	$0.881487\pi$
$492$	−2.50360	−	0.572850i	−0.112871	−	0.0258261i
$493$	−7.70088	−	6.46180i	−0.346830	−	0.291025i
$494$	1.68882	−	2.92512i	0.0759837	−	0.131608i
$495$	2.60063	+	5.78019i	0.116890	+	0.259800i
$496$	3.33108	+	5.76961i	0.149570	+	0.259063i
$497$	8.27013	−	46.9023i	0.370966	−	2.10385i
$498$	−33.7530	+	4.21133i	−1.51251	+	0.188714i
$499$	−10.9338	−	3.97957i	−0.489463	−	0.178150i	0.0854858	−	0.996339i	$-0.472756\pi$
$499$	−10.9338	−	3.97957i	−0.489463	−	0.178150i	−0.574949	+	0.818189i	$0.694978\pi$
$500$	−7.64382	−	2.78212i	−0.341842	−	0.124420i
$501$	−1.46576	+	3.47196i	−0.0654851	+	0.155116i
$502$	−6.25832	+	35.4927i	−0.279323	+	1.58412i
$503$	18.8996	+	32.7350i	0.842689	+	1.45958i	0.887613	+	0.460590i	$0.152362\pi$
$503$	18.8996	+	32.7350i	0.842689	+	1.45958i	−0.0449234	+	0.998990i	$0.514304\pi$
$504$	−16.1477	−	16.5912i	−0.719277	−	0.739029i
$505$	−9.82831	+	17.0231i	−0.437354	+	0.757519i
$506$	14.0360	+	11.7776i	0.623977	+	0.523579i
$507$	−6.35179	−	20.6314i	−0.282093	−	0.916274i
$508$	0.153297	+	0.869388i	0.00680143	+	0.0385729i
$509$	18.0585	−	15.1528i	0.800427	−	0.671638i	−0.147875	−	0.989006i	$-0.547243\pi$
$509$	18.0585	−	15.1528i	0.800427	−	0.671638i	0.948302	+	0.317368i	$0.102799\pi$
$510$	5.53141	−	2.83203i	0.244935	−	0.125404i
$511$	36.3193	−	13.2191i	1.60667	−	0.584780i
$512$	2.26711			0.100193
$513$	−11.1285	−	8.90415i	−0.491336	−	0.393128i
$514$	−24.8548			−1.09630
$515$	−16.7843	+	6.10899i	−0.739605	+	0.269194i
$516$	0.362352	−	7.18272i	0.0159517	−	0.316202i
$517$	−2.44828	+	2.05435i	−0.107675	+	0.0903503i
$518$	−3.87485	−	21.9753i	−0.170251	−	0.965541i
$519$	−20.7076	+	22.2934i	−0.908963	+	0.978572i
$520$	−1.25151	−	1.05014i	−0.0548822	−	0.0460517i
$521$	−3.93474	+	6.81517i	−0.172384	+	0.298578i	−0.939253	−	0.343226i	$-0.888480\pi$
$521$	−3.93474	+	6.81517i	−0.172384	+	0.298578i	0.766869	+	0.641804i	$0.221814\pi$
$522$	−24.1578	−	11.6658i	−1.05736	−	0.510600i
$523$	−16.6467	−	28.8330i	−0.727911	−	1.26078i	−0.957765	−	0.287554i	$-0.907158\pi$
$523$	−16.6467	−	28.8330i	−0.727911	−	1.26078i	0.229854	−	0.973225i	$-0.426175\pi$
$524$	1.09517	−	6.21099i	0.0478425	−	0.271328i
$525$	−15.2135	−	20.1071i	−0.663973	−	0.877547i
$526$	−4.42707	−	1.61132i	−0.193029	−	0.0702570i
$527$	−2.38048	−	0.866425i	−0.103695	−	0.0377421i
$528$	−9.71430	−	12.8390i	−0.422761	−	0.558746i
$529$	1.90355	−	10.7955i	0.0827628	−	0.469371i
$530$	2.70080	+	4.67792i	0.117315	+	0.203196i
$531$	27.9309	−	18.9990i	1.21210	−	0.824485i
$532$	4.42516	−	7.66461i	0.191855	−	0.332303i
$533$	−1.00811	−	0.845902i	−0.0436659	−	0.0366401i
$534$	−11.3510	+	12.2203i	−0.491207	+	0.528824i
$535$	3.24221	+	18.3875i	0.140173	+	0.794961i
$536$	2.85695	−	2.39727i	0.123402	−	0.103546i
$537$	0.0876573	−	1.73759i	0.00378269	−	0.0749823i
$538$	0.563150	−	0.204970i	0.0242791	−	0.00883687i
$539$	−15.4868			−0.667062
$540$	3.63778	−	3.19992i	0.156545	−	0.137703i
$541$	22.4283			0.964266			0.482133	−	0.876098i	$-0.339862\pi$
$541$	22.4283			0.964266			0.482133	+	0.876098i	$0.339862\pi$
$542$	19.1861	−	6.98318i	0.824115	−	0.299953i
$543$	32.6434	−	16.7131i	1.40086	−	0.717228i
$544$	−6.37614	+	5.35022i	−0.273375	+	0.229389i
$545$	0.925490	+	5.24872i	0.0396436	+	0.224830i
$546$	2.45319	+	7.96827i	0.104987	+	0.341011i
$547$	−16.0036	−	13.4286i	−0.684262	−	0.574164i	0.232986	−	0.972480i	$-0.425150\pi$
$547$	−16.0036	−	13.4286i	−0.684262	−	0.574164i	−0.917248	+	0.398316i	$0.869595\pi$
$548$	−6.45948	+	11.1881i	−0.275935	+	0.477934i
$549$	−4.26648	+	15.1016i	−0.182089	+	0.644519i
$550$	−5.85447	−	10.1402i	−0.249635	−	0.432381i
$551$	−2.53384	+	14.3701i	−0.107945	+	0.612188i
$552$	−7.75070	+	18.3592i	−0.329892	+	0.781420i
$553$	45.3744	+	16.5149i	1.92952	+	0.702286i
$554$	−39.4727	−	14.3669i	−1.67703	−	0.610390i
$555$	−6.59313	+	0.822620i	−0.279863	+	0.0349183i
$556$	1.24089	−	7.03744i	0.0526255	−	0.298454i
$557$	−4.28920	−	7.42911i	−0.181739	−	0.314782i	0.760734	−	0.649064i	$-0.224839\pi$
$557$	−4.28920	−	7.42911i	−0.181739	−	0.314782i	−0.942473	+	0.334283i	$0.891506\pi$
$558$	−6.72597	−	0.680352i	−0.284733	−	0.0288016i
$559$	1.84254	−	3.19137i	0.0779311	−	0.134981i
$560$	−16.8085	−	14.1040i	−0.710291	−	0.596005i
$561$	5.96770	+	1.36547i	0.251957	+	0.0576502i
$562$	2.13745	+	12.1221i	0.0901630	+	0.511340i
$563$	−12.0383	+	10.1013i	−0.507354	+	0.425720i	−0.860197	−	0.509962i	$-0.829659\pi$
$563$	−12.0383	+	10.1013i	−0.507354	+	0.425720i	0.352843	+	0.935682i	$0.385215\pi$
$564$	2.05145	+	1.32653i	0.0863817	+	0.0558572i
$565$	21.1699	−	7.70522i	0.890625	−	0.324161i
$566$	−24.1851			−1.01658
$567$	34.7986	−	5.16841i	1.46140	−	0.217053i
$568$	24.0545			1.00930
$569$	−11.9085	+	4.33435i	−0.499231	+	0.181705i	−0.579348	−	0.815080i	$-0.696693\pi$
$569$	−11.9085	+	4.33435i	−0.499231	+	0.181705i	0.0801169	+	0.996785i	$0.474471\pi$
$570$	−7.57449	−	4.89791i	−0.317260	−	0.205151i
$571$	−20.1644	+	16.9199i	−0.843852	+	0.708076i	−0.958427	−	0.285339i	$-0.907894\pi$
$571$	−20.1644	+	16.9199i	−0.843852	+	0.708076i	0.114575	+	0.993415i	$0.463449\pi$
$572$	0.196419	+	1.11394i	0.00821267	+	0.0465764i
$573$	16.5944	+	3.79697i	0.693241	+	0.158621i
$574$	−9.04155	−	7.58676i	−0.377387	−	0.316665i
$575$	−10.8516	+	18.7954i	−0.452541	+	0.783824i
$576$	4.44607	−	6.17008i	0.185253	−	0.257087i
$577$	11.0577	+	19.1525i	0.460338	+	0.797329i	0.998978	−	0.0452074i	$-0.0143949\pi$
$577$	11.0577	+	19.1525i	0.460338	+	0.797329i	−0.538640	+	0.842536i	$0.681062\pi$
$578$	−3.91983	+	22.2304i	−0.163043	+	0.924665i
$579$	−19.1742	+	2.39236i	−0.796854	+	0.0994230i
$580$	−4.66116	−	1.69652i	−0.193544	−	0.0704444i
$581$	−42.9144	−	15.6196i	−1.78039	−	0.648009i
$582$	0.388822	−	0.921009i	0.0161172	−	0.0381771i
$583$	−0.924041	+	5.24050i	−0.0382699	+	0.217039i
$584$	9.76057	+	16.9058i	0.403895	+	0.699567i
$585$	2.40640	−	0.609985i	0.0994923	−	0.0252198i
$586$	12.1156	−	20.9848i	0.500491	−	0.866876i
$587$	10.9568	+	9.19388i	0.452237	+	0.379472i	0.840265	−	0.542176i	$-0.182399\pi$
$587$	10.9568	+	9.19388i	0.452237	+	0.379472i	−0.388028	+	0.921647i	$0.626844\pi$
$588$	3.48318	+	11.3138i	0.143644	+	0.466574i
$589$	0.638517	+	3.62121i	0.0263097	+	0.149209i
$590$	16.3773	−	13.7422i	0.674243	−	0.565757i
$591$	−14.0142	+	7.17514i	−0.576468	+	0.295146i
$592$	15.8593	−	5.77231i	0.651813	−	0.237241i
$593$	47.7300			1.96004			0.980018	−	0.198908i	$-0.0637397\pi$
$593$	47.7300			1.96004			0.980018	+	0.198908i	$0.0637397\pi$
$594$	16.3326	−	0.380910i	0.670136	−	0.0156289i
$595$	8.34334			0.342044
$596$	1.91115	−	0.695601i	0.0782837	−	0.0284929i
$597$	−1.28229	+	25.4182i	−0.0524808	+	1.04030i
$598$	5.49746	−	4.61291i	0.224808	−	0.188636i
$599$	−0.0867493	−	0.491980i	−0.00354448	−	0.0201018i	0.982984	−	0.183690i	$-0.0588043\pi$
$599$	−0.0867493	−	0.491980i	−0.00354448	−	0.0201018i	−0.986529	+	0.163588i	$0.947693\pi$
$600$	8.66697	−	9.33069i	0.353828	−	0.380924i
$601$	−12.9669	−	10.8805i	−0.528931	−	0.443826i	0.338801	−	0.940858i	$-0.389979\pi$
$601$	−12.9669	−	10.8805i	−0.528931	−	0.443826i	−0.867732	+	0.497032i	$0.834423\pi$
$602$	16.5254	−	28.6229i	0.673527	−	1.16658i
$603$	0.417415	+	5.65169i	0.0169985	+	0.230155i
$604$	4.33923	+	7.51577i	0.176561	+	0.305812i
$605$	1.47135	−	8.34443i	0.0598188	−	0.339249i
$606$	30.5702	+	40.4035i	1.24183	+	1.64128i
$607$	−0.652741	−	0.237578i	−0.0264939	−	0.00964301i	0.328739	−	0.944421i	$-0.393376\pi$
$607$	−0.652741	−	0.237578i	−0.0264939	−	0.00964301i	−0.355233	+	0.934778i	$0.615599\pi$
$608$	11.3531	+	4.13218i	0.460427	+	0.167582i
$609$	−21.7326	−	28.7231i	−0.880649	−	1.16392i
$610$	−1.72462	+	9.78083i	−0.0698280	+	0.396014i
$611$	0.625887	+	1.08407i	0.0253207	+	0.0438567i
$612$	−0.344674	−	4.66680i	−0.0139326	−	0.188644i
$613$	16.3317	−	28.2873i	0.659630	−	1.14251i	−0.321081	−	0.947052i	$-0.604046\pi$
$613$	16.3317	−	28.2873i	0.659630	−	1.14251i	0.980711	−	0.195461i	$-0.0626204\pi$
$614$	−39.1866	−	32.8815i	−1.58144	−	1.32699i
$615$	−2.39178	+	2.57495i	−0.0964460	+	0.103832i
$616$	−2.50660	−	14.2157i	−0.100994	−	0.572765i
$617$	17.5305	−	14.7098i	0.705751	−	0.592195i	−0.217652	−	0.976026i	$-0.569840\pi$
$617$	17.5305	−	14.7098i	0.705751	−	0.592195i	0.923403	+	0.383831i	$0.125395\pi$
$618$	−2.31958	+	45.9799i	−0.0933074	+	1.84958i
$619$	−7.97398	+	2.90229i	−0.320501	+	0.116653i	−0.497261	−	0.867601i	$-0.665661\pi$
$619$	−7.97398	+	2.90229i	−0.320501	+	0.116653i	0.176759	+	0.984254i	$0.443439\pi$
$620$	−1.24998			−0.0502002
$621$	−15.7481	−	25.8645i	−0.631951	−	1.03791i
$622$	−23.5254			−0.943282
$623$	−21.0427	+	7.65892i	−0.843058	+	0.306848i
$624$	−5.61293	+	2.87377i	−0.224697	+	0.115043i
$625$	5.73752	−	4.81435i	0.229501	−	0.192574i
$626$	6.44708	+	36.5632i	0.257677	+	1.46136i
$627$	−2.61465	−	8.49272i	−0.104419	−	0.339167i
$628$	0.227611	+	0.190988i	0.00908267	+	0.00762127i
$629$	−3.20872	+	5.55767i	−0.127940	+	0.221599i
$630$	21.5826	−	5.47086i	0.859871	−	0.217964i
$631$	−0.795865	−	1.37848i	−0.0316829	−	0.0548763i	0.849749	−	0.527187i	$-0.176753\pi$
$631$	−0.795865	−	1.37848i	−0.0316829	−	0.0548763i	−0.881432	+	0.472311i	$0.843420\pi$
$632$	−4.23496	+	24.0176i	−0.168458	+	0.955370i
$633$	−5.29373	+	12.5393i	−0.210407	+	0.498394i
$634$	−27.4662	−	9.99688i	−1.09082	−	0.397027i
$635$	1.13515	+	0.413160i	0.0450469	+	0.0163957i
$636$	4.03626	−	0.503601i	0.160048	−	0.0199691i
$637$	−1.05329	+	5.97352i	−0.0417330	+	0.236680i
$638$	−8.36313	−	14.4854i	−0.331099	−	0.573481i
$639$	−21.3687	+	29.6546i	−0.845333	+	1.17312i
$640$	7.38198	−	12.7860i	0.291798	−	0.505409i
$641$	16.6038	+	13.9322i	0.655809	+	0.550289i	0.908827	−	0.417173i	$-0.136979\pi$
$641$	16.6038	+	13.9322i	0.655809	+	0.550289i	−0.253019	+	0.967461i	$0.581423\pi$
$642$	46.9130	+	10.7342i	1.85151	+	0.423644i
$643$	−1.19853	−	6.79720i	−0.0472654	−	0.268056i	0.952012	−	0.306060i	$-0.0990109\pi$
$643$	−1.19853	−	6.79720i	−0.0472654	−	0.268056i	−0.999278	+	0.0380047i	$0.987900\pi$
$644$	14.4048	−	12.0871i	0.567629	−	0.476297i
$645$	−8.26393	−	5.34372i	−0.325392	−	0.210409i
$646$	−8.18679	+	2.97975i	−0.322105	+	0.117237i
$647$	−6.18972			−0.243343			−0.121671	−	0.992570i	$-0.538825\pi$
$647$	−6.18972			−0.243343			−0.121671	+	0.992570i	$0.538825\pi$
$648$	5.62277	+	16.8555i	0.220883	+	0.662146i
$649$	21.0614			0.826733
$650$	−4.30945	+	1.56851i	−0.169030	+	0.0615220i
$651$	−7.62182	−	4.92851i	−0.298723	−	0.193164i
$652$	9.24396	−	7.75660i	0.362021	−	0.303772i
$653$	−4.72574	−	26.8010i	−0.184933	−	1.04881i	−0.926042	−	0.377421i	$-0.876811\pi$
$653$	−4.72574	−	26.8010i	−0.184933	−	1.04881i	0.741109	−	0.671384i	$-0.234300\pi$
$654$	13.3913	+	3.06407i	0.523642	+	0.119815i
$655$	−6.61100	−	5.54729i	−0.258313	−	0.216751i
$656$	4.46347	−	7.73096i	0.174269	−	0.301843i
$657$	−29.5124	−	2.98527i	−1.15139	−	0.116467i
$658$	5.61348	+	9.72283i	0.218836	+	0.379035i
$659$	0.917209	−	5.20175i	0.0357294	−	0.202631i	−0.961718	−	0.274043i	$-0.911639\pi$
$659$	0.917209	−	5.20175i	0.0357294	−	0.202631i	0.997447	+	0.0714110i	$0.0227502\pi$
$660$	2.99748	−	0.373993i	0.116677	−	0.0145577i
$661$	−10.9616	−	3.98968i	−0.426355	−	0.155181i	0.119925	−	0.992783i	$-0.461734\pi$
$661$	−10.9616	−	3.98968i	−0.426355	−	0.155181i	−0.546280	+	0.837602i	$0.683957\pi$
$662$	−1.36496	−	0.496803i	−0.0530505	−	0.0193088i
$663$	0.932564	−	2.20898i	0.0362178	−	0.0857897i
$664$	4.00536	−	22.7155i	0.155438	−	0.881533i
$665$	−6.05527	−	10.4880i	−0.234813	−	0.406708i
$666$	−4.65609	+	16.4806i	−0.180420	+	0.638611i
$667$	−15.5015	+	26.8494i	−0.600220	+	1.03961i
$668$	1.37588	+	1.15450i	0.0532345	+	0.0446690i
$669$	−4.45470	−	14.4694i	−0.172229	−	0.559421i
$670$	0.622812	+	3.53214i	0.0240613	+	0.136459i
$671$	−7.49510	+	6.28913i	−0.289345	+	0.242789i
$672$	−26.5454	+	13.5910i	−1.02401	+	0.524283i
$673$	−46.1412	+	16.7940i	−1.77861	+	0.647362i	−0.778814	+	0.627255i	$0.784178\pi$
$673$	−46.1412	+	16.7940i	−1.77861	+	0.647362i	−0.999798	+	0.0201071i	$0.993599\pi$
$674$	0.703510			0.0270982
$675$	3.80371	+	18.9736i	0.146405	+	0.730295i
$676$	−10.2880			−0.395693
$677$	21.2550	−	7.73617i	0.816894	−	0.297325i	0.100426	−	0.994945i	$-0.467980\pi$
$677$	21.2550	−	7.73617i	0.816894	−	0.297325i	0.716469	+	0.697619i	$0.245757\pi$
$678$	2.92567	−	57.9941i	0.112360	−	2.22725i
$679$	1.02822	−	0.862775i	0.0394593	−	0.0331103i
$680$	0.731752	+	4.14997i	0.0280614	+	0.159144i
$681$	4.79576	−	5.16302i	0.183774	−	0.197847i
$682$	−3.22884	−	2.70931i	−0.123639	−	0.103745i
$683$	8.56931	−	14.8425i	0.327896	−	0.567932i	−0.654198	−	0.756323i	$-0.726994\pi$
$683$	8.56931	−	14.8425i	0.327896	−	0.567932i	0.982094	+	0.188391i	$0.0603272\pi$
$684$	−5.61626	+	3.82025i	−0.214743	+	0.146071i
$685$	8.83897	+	15.3095i	0.337720	+	0.584947i
$686$	−1.46007	+	8.28045i	−0.0557456	+	0.316149i
$687$	−16.8841	−	22.3151i	−0.644169	−	0.851374i
$688$	23.4900	+	8.54966i	0.895548	+	0.325953i
$689$	1.95851	+	0.712838i	0.0746132	+	0.0271570i
$690$	−11.5636	−	15.2832i	−0.440219	−	0.581820i
$691$	3.17011	−	17.9786i	0.120597	−	0.683937i	−0.863230	−	0.504811i	$-0.831562\pi$
$691$	3.17011	−	17.9786i	0.120597	−	0.683937i	0.983826	−	0.179126i	$-0.0573268\pi$
$692$	7.25049	+	12.5582i	0.275622	+	0.477392i
$693$	19.7520	+	9.53826i	0.750315	+	0.362328i
$694$	−19.6749	+	34.0779i	−0.746848	+	1.29358i
$695$	−7.49068	−	6.28543i	−0.284138	−	0.238420i
$696$	12.3808	−	13.3289i	0.469293	−	0.505232i
$697$	0.589436	+	3.34286i	0.0223265	+	0.126620i
$698$	27.2679	−	22.8805i	1.03210	−	0.866038i
$699$	1.50214	−	29.7762i	0.0568163	−	1.12624i
$700$	−11.2919	+	4.10991i	−0.426793	+	0.155340i
$701$	−2.92075			−0.110315			−0.0551575	−	0.998478i	$-0.517566\pi$
$701$	−2.92075			−0.110315			−0.0551575	+	0.998478i	$0.517566\pi$
$702$	0.963899	−	6.32570i	0.0363800	−	0.238748i
$703$	9.31505			0.351324
$704$	4.45570	−	1.62174i	0.167931	−	0.0611218i
$705$	2.97558	−	1.52347i	0.112067	−	0.0573771i
$706$	30.3171	−	25.4391i	1.14100	−	0.957412i
$707$	11.8123	+	66.9906i	0.444246	+	2.51944i
$708$	−4.73699	−	15.3864i	−0.178027	−	0.578255i
$709$	23.0023	+	19.3012i	0.863868	+	0.724872i	0.962798	−	0.270223i	$-0.0870974\pi$
$709$	23.0023	+	19.3012i	0.863868	+	0.724872i	−0.0989295	+	0.995094i	$0.531542\pi$
$710$	−11.5665	+	20.0338i	−0.434084	+	0.751856i
$711$	−25.8471	−	26.5569i	−0.969342	−	0.995961i
$712$	−5.65509	−	9.79490i	−0.211933	−	0.367079i
$713$	−1.35665	+	7.69393i	−0.0508068	+	0.288140i
$714$	8.36402	−	19.8120i	0.313016	−	0.741445i
$715$	1.45446	+	0.529381i	0.0543938	+	0.0197977i
$716$	−0.779152	−	0.283588i	−0.0291183	−	0.0105982i
$717$	−2.63900	+	0.329266i	−0.0985552	+	0.0122967i
$718$	−3.05341	+	17.3168i	−0.113952	+	0.646256i
$719$	−20.0285	−	34.6903i	−0.746936	−	1.29373i	−0.949285	−	0.314418i	$-0.898191\pi$
$719$	−20.0285	−	34.6903i	−0.746936	−	1.29373i	0.202349	−	0.979314i	$-0.435143\pi$
$720$	6.90951	+	15.3572i	0.257502	+	0.572327i
$721$	−30.9059	+	53.5306i	−1.15100	+	1.99358i
$722$	−14.7781	−	12.4003i	−0.549983	−	0.461490i
$723$	9.32289	+	2.13317i	0.346722	+	0.0793335i
$724$	−3.03499	−	17.2123i	−0.112794	−	0.639689i
$725$	15.1770	−	12.7350i	0.563659	−	0.472966i
$726$	−18.3396	−	11.8590i	−0.680645	−	0.440127i
$727$	1.44598	−	0.526294i	0.0536285	−	0.0195192i	−0.315067	−	0.949070i	$-0.602027\pi$
$727$	1.44598	−	0.526294i	0.0536285	−	0.0195192i	0.368695	+	0.929550i	$0.379805\pi$
$728$	−5.65371			−0.209540
$729$	−25.7746	−	8.04171i	−0.954615	−	0.297841i
$730$	−18.7734			−0.694834
$731$	−8.93196	+	3.25097i	−0.330361	+	0.120241i
$732$	6.28025	+	4.06101i	0.232125	+	0.150099i
$733$	−1.15818	+	0.971827i	−0.0427783	+	0.0358952i	−0.663926	−	0.747798i	$-0.731111\pi$
$733$	−1.15818	+	0.971827i	−0.0427783	+	0.0358952i	0.621148	+	0.783693i	$0.286667\pi$
$734$	6.20502	+	35.1904i	0.229031	+	1.29890i
$735$	15.7905	+	3.61303i	0.582442	+	0.133269i
$736$	19.6642	+	16.5002i	0.724830	+	0.608205i
$737$	−1.76667	+	3.05997i	−0.0650762	+	0.112715i
$738$	3.71672	+	8.26082i	0.136814	+	0.304085i
$739$	−10.6779	−	18.4946i	−0.392792	−	0.680336i	0.600024	−	0.799982i	$-0.295157\pi$
$739$	−10.6779	−	18.4946i	−0.392792	−	0.680336i	−0.992817	+	0.119646i	$0.961824\pi$
$740$	−0.549863	+	3.11843i	−0.0202134	+	0.114636i
$741$	−3.45362	+	0.430906i	−0.126872	+	0.0158297i
$742$	17.5655	+	6.39333i	0.644851	+	0.234707i
$743$	19.1028	+	6.95284i	0.700812	+	0.255075i	0.667758	−	0.744379i	$-0.267254\pi$
$743$	19.1028	+	6.95284i	0.700812	+	0.255075i	0.0330547	+	0.999454i	$0.489476\pi$
$744$	1.78297	−	4.22334i	0.0653667	−	0.154835i
$745$	0.483262	−	2.74072i	0.0177054	−	0.100412i
$746$	−1.94153	−	3.36282i	−0.0710843	−	0.123122i
$747$	24.4458	+	25.1171i	0.894425	+	0.918987i
$748$	1.45880	−	2.52672i	0.0533391	−	0.0923860i
$749$	49.4970	+	41.5329i	1.80858	+	1.51758i
$750$	8.44177	+	27.4200i	0.308250	+	1.00124i
$751$	0.740289	+	4.19839i	0.0270135	+	0.153201i	0.995331	−	0.0965214i	$-0.0307716\pi$
$751$	0.740289	+	4.19839i	0.0270135	+	0.153201i	−0.968317	+	0.249723i	$0.919661\pi$
$752$	−6.50474	+	5.45813i	−0.237204	+	0.199037i
$753$	33.0560	−	16.9244i	1.20463	−	0.616758i
$754$	−6.15606	+	2.24062i	−0.224191	+	0.0815987i
$755$	11.8754			0.432189
$756$	2.52567	−	16.5750i	0.0918578	−	0.602827i
$757$	54.3419			1.97509			0.987546	−	0.157332i	$-0.0502892\pi$
$757$	54.3419			1.97509			0.987546	+	0.157332i	$0.0502892\pi$
$758$	−19.8294	+	7.21730i	−0.720235	+	0.262144i
$759$	0.951252	−	18.8562i	0.0345282	−	0.684435i
$760$	4.68566	−	3.93174i	0.169967	−	0.142619i
$761$	3.15364	+	17.8852i	0.114319	+	0.648338i	0.987085	+	0.160198i	$0.0512133\pi$
$761$	3.15364	+	17.8852i	0.114319	+	0.648338i	−0.872765	+	0.488140i	$0.837676\pi$
$762$	2.11904	−	2.28132i	0.0767649	−	0.0826435i
$763$	14.1289	+	11.8556i	0.511502	+	0.429201i
$764$	4.05650	−	7.02606i	0.146759	−	0.254194i
$765$	−5.76618	−	2.78450i	−0.208477	−	0.100674i
$766$	16.5188	+	28.6113i	0.596847	+	1.03377i
$767$	1.43244	−	8.12376i	0.0517224	−	0.293332i
$768$	−17.6625	−	23.3438i	−0.637340	−	0.842348i
$769$	−23.3558	−	8.50082i	−0.842232	−	0.306547i	−0.115363	−	0.993323i	$-0.536803\pi$
$769$	−23.3558	−	8.50082i	−0.842232	−	0.306547i	−0.726869	+	0.686776i	$0.759025\pi$
$770$	13.0448	+	4.74793i	0.470103	+	0.171104i
$771$	15.4530	+	20.4236i	0.556526	+	0.735539i
$772$	−1.59912	+	9.06906i	−0.0575536	+	0.326403i
$773$	−19.2416	−	33.3274i	−0.692071	−	1.19870i	−0.971158	−	0.238437i	$-0.923365\pi$
$773$	−19.2416	−	33.3274i	−0.692071	−	1.19870i	0.279087	−	0.960266i	$-0.409968\pi$
$774$	−20.9735	+	14.2664i	−0.753878	+	0.512797i
$775$	2.49629	−	4.32369i	0.0896692	−	0.155312i
$776$	0.519323	+	0.435764i	0.0186426	+	0.0156430i
$777$	−15.6484	+	16.8468i	−0.561385	+	0.604376i
$778$	−5.49991	−	31.1916i	−0.197181	−	1.11827i
$779$	3.77436	−	3.16707i	0.135231	−	0.113472i
$780$	0.0596099	−	1.18162i	0.00213438	−	0.0423087i
$781$	−21.4150	+	7.79443i	−0.766290	+	0.278907i
$782$	−18.5107			−0.661940
$783$	5.43361	+	27.1039i	0.194181	+	0.968615i
$784$	−41.1462			−1.46951
$785$	0.382058	−	0.139058i	0.0136362	−	0.00496319i
$786$	−19.7999	+	10.1374i	−0.706239	+	0.361588i
$787$	−0.821566	+	0.689376i	−0.0292857	+	0.0245736i	−0.657313	−	0.753618i	$-0.728307\pi$
$787$	−0.821566	+	0.689376i	−0.0292857	+	0.0245736i	0.628027	+	0.778191i	$0.283863\pi$
$788$	1.30296	+	7.38944i	0.0464159	+	0.263238i
$789$	1.42840	+	4.63962i	0.0508523	+	0.165175i
$790$	−17.9668	−	15.0759i	−0.639229	−	0.536377i
$791$	38.9814	−	67.5177i	1.38602	−	2.40065i
$792$	−3.01198	+	10.6612i	−0.107026	+	0.378828i
$793$	1.91607	+	3.31873i	0.0680417	+	0.117852i
$794$	5.87212	−	33.3025i	0.208394	−	1.18186i
$795$	2.16476	−	5.12770i	0.0767761	−	0.181861i
$796$	11.3978	+	4.14846i	0.403985	+	0.147038i
$797$	−23.7246	−	8.63505i	−0.840369	−	0.305869i	−0.114262	−	0.993451i	$-0.536450\pi$
$797$	−23.7246	−	8.63505i	−0.840369	−	0.305869i	−0.726107	+	0.687581i	$0.758672\pi$
$798$	−30.9750	+	3.86473i	−1.09650	+	0.136810i
$799$	0.560674	−	3.17974i	0.0198352	−	0.112491i
$800$	−8.20198	−	14.2063i	−0.289984	−	0.502267i
$801$	17.0989	+	1.72961i	0.604161	+	0.0611127i
$802$	25.8908	−	44.8442i	0.914237	−	1.58350i
$803$	−14.1676	−	11.8880i	−0.499963	−	0.419519i
$804$	2.63280	+	0.602410i	0.0928515	+	0.0212454i
$805$	−4.46815	−	25.3401i	−0.157482	−	0.893122i
$806$	−1.26463	+	1.06115i	−0.0445448	+	0.0373775i
$807$	−0.518556	−	0.335315i	−0.0182540	−	0.0118036i
$808$	−32.2851	+	11.7508i	−1.13579	+	0.413392i
$809$	−11.7337			−0.412536			−0.206268	−	0.978495i	$-0.566132\pi$
$809$	−11.7337			−0.412536			−0.206268	+	0.978495i	$0.566132\pi$
$810$	−16.7418	−	3.42199i	−0.588248	−	0.120236i
$811$	−38.4085			−1.34871			−0.674353	−	0.738409i	$-0.735577\pi$
$811$	−38.4085			−1.34871			−0.674353	+	0.738409i	$0.735577\pi$
$812$	−16.1305	+	5.87103i	−0.566070	+	0.206033i
$813$	−17.6668	−	11.4239i	−0.619603	−	0.400655i
$814$	−8.17953	+	6.86344i	−0.286693	+	0.240564i
$815$	−2.86733	−	16.2615i	−0.100438	−	0.569614i
$816$	15.8553	+	3.62786i	0.555048	+	0.127001i
$817$	10.5691	+	8.86853i	0.369766	+	0.310271i
$818$	−33.3594	+	57.7802i	−1.16639	+	2.02024i
$819$	5.02246	−	6.96996i	0.175499	−	0.243550i
$820$	0.837450	+	1.45051i	0.0292450	+	0.0506539i
$821$	4.64197	−	26.3259i	0.162006	−	0.918781i	−0.790092	−	0.612988i	$-0.789967\pi$
$821$	4.64197	−	26.3259i	0.162006	−	0.918781i	0.952098	−	0.305793i	$-0.0989216\pi$
$822$	45.2147	−	5.64141i	1.57704	−	0.196767i
$823$	−4.10107	−	1.49267i	−0.142954	−	0.0520311i	0.269552	−	0.962986i	$-0.413124\pi$
$823$	−4.10107	−	1.49267i	−0.142954	−	0.0520311i	−0.412506	+	0.910955i	$0.635347\pi$
$824$	−29.3367	−	10.6777i	−1.02199	−	0.371974i
$825$	−4.69251	+	11.1152i	−0.163372	+	0.386983i
$826$	12.8473	−	72.8608i	0.447015	−	2.53515i
$827$	19.5727	+	33.9009i	0.680610	+	1.17885i	0.974795	+	0.223102i	$0.0716184\pi$
$827$	19.5727	+	33.9009i	0.680610	+	1.17885i	−0.294185	+	0.955748i	$0.595048\pi$
$828$	−13.9893	+	3.54606i	−0.486160	+	0.123234i
$829$	16.4433	−	28.4807i	0.571101	−	0.989176i	−0.425352	−	0.905028i	$-0.639850\pi$
$829$	16.4433	−	28.4807i	0.571101	−	0.989176i	0.996453	−	0.0841481i	$-0.0268169\pi$
$830$	16.9927	+	14.2586i	0.589826	+	0.494922i
$831$	12.7359	+	41.3678i	0.441803	+	1.43503i
$832$	−0.322492	−	1.82894i	−0.0111804	−	0.0634072i
$833$	11.9853	−	10.0568i	0.415264	−	0.348448i
$834$	−22.4345	+	11.4863i	−0.776844	+	0.397737i
$835$	2.30950	−	0.840588i	0.0799234	−	0.0290898i
$836$	−4.23496			−0.146469
$837$	3.62269	+	5.94986i	0.125219	+	0.205657i
$838$	25.9552			0.896607
$839$	−29.7322	+	10.8216i	−1.02647	+	0.373604i	−0.799735	−	0.600353i	$-0.795027\pi$
$839$	−29.7322	+	10.8216i	−1.02647	+	0.373604i	−0.226734	+	0.973957i	$0.572805\pi$
$840$	−0.760715	+	15.0792i	−0.0262471	+	0.520283i
$841$	−0.534920	+	0.448851i	−0.0184455	+	0.0154776i
$842$	−5.28131	−	29.9518i	−0.182006	−	1.03221i
$843$	8.63203	−	9.29308i	0.297303	−	0.320071i
$844$	4.96914	+	4.16961i	0.171045	+	0.143524i
$845$	−7.03892	+	12.1918i	−0.242146	+	0.419410i
$846$	−0.634651	−	8.59300i	−0.0218197	−	0.295434i
$847$	−14.6612	−	25.3939i	−0.503764	−	0.872545i
$848$	−2.45505	+	13.9233i	−0.0843066	+	0.478127i
$849$	15.0366	+	19.8734i	0.516056	+	0.682052i
$850$	11.1157	+	4.04577i	0.381264	+	0.138769i
$851$	18.5980	+	6.76910i	0.637530	+	0.232042i
$852$	10.5107	+	13.8916i	0.360091	+	0.475919i
$853$	−0.982440	+	5.57169i	−0.0336381	+	0.190771i	−0.996997	−	0.0774461i	$-0.975323\pi$
$853$	−0.982440	+	5.57169i	−0.0336381	+	0.190771i	0.963358	+	0.268217i	$0.0864345\pi$
$854$	17.1849	+	29.7652i	0.588057	+	1.01854i
$855$	0.684599	+	9.26928i	0.0234128	+	0.317003i
$856$	−16.3173	+	28.2624i	−0.557715	+	0.965990i
$857$	−31.5690	−	26.4895i	−1.07838	−	0.904864i	−0.0825904	−	0.996584i	$-0.526319\pi$
$857$	−31.5690	−	26.4895i	−1.07838	−	0.904864i	−0.995785	+	0.0917193i	$0.970764\pi$
$858$	2.71513	−	2.92305i	0.0926929	−	0.0997913i
$859$	6.22605	+	35.3097i	0.212430	+	1.20475i	0.885311	+	0.465000i	$0.153946\pi$
$859$	6.22605	+	35.3097i	0.212430	+	1.20475i	−0.672880	+	0.739751i	$0.734943\pi$
$860$	−3.59284	+	3.01475i	−0.122515	+	0.102802i
$861$	−0.612766	+	12.1465i	−0.0208830	+	0.413953i
$862$	45.7566	−	16.6541i	1.55848	−	0.567239i
$863$	20.9694			0.713806			0.356903	−	0.934142i	$-0.383833\pi$
$863$	20.9694			0.713806			0.356903	+	0.934142i	$0.383833\pi$
$864$	22.8817	−	0.533646i	0.778451	−	0.0181550i
$865$	19.8427			0.674673
$866$	59.3753	−	21.6108i	2.01765	−	0.734366i
$867$	20.7043	−	10.6004i	0.703153	−	0.360008i
$868$	−3.31367	+	2.78050i	−0.112473	+	0.0943764i
$869$	−4.01223	−	22.7545i	−0.136106	−	0.771893i
$870$	5.14775	+	16.7206i	0.174525	+	0.566880i
$871$	1.06013	+	0.889553i	0.0359210	+	0.0301413i
$872$	−4.65778	+	8.06751i	−0.157732	+	0.273201i
$873$	−0.998554	+	0.253118i	−0.0337959	+	0.00856675i
$874$	13.4343	+	23.2689i	0.454422	+	0.787082i
$875$	−6.68887	+	37.9345i	−0.226125	+	1.28242i
$876$	−5.49828	+	13.0239i	−0.185770	+	0.440035i
$877$	−19.2735	−	7.01498i	−0.650819	−	0.236879i	−0.00455171	−	0.999990i	$-0.501449\pi$
$877$	−19.2735	−	7.01498i	−0.650819	−	0.236879i	−0.646268	+	0.763111i	$0.723671\pi$
$878$	−16.2117	−	5.90057i	−0.547117	−	0.199134i
$879$	−24.7763	+	3.09132i	−0.835684	+	0.104268i
$880$	−1.82321	+	10.3399i	−0.0614604	+	0.348559i
$881$	19.1438	+	33.1581i	0.644972	+	1.11712i	0.984308	+	0.176459i	$0.0564644\pi$
$881$	19.1438	+	33.1581i	0.644972	+	1.11712i	−0.339336	+	0.940665i	$0.610202\pi$
$882$	24.4091	−	33.8740i	0.821897	−	1.14060i
$883$	8.72326	−	15.1091i	0.293561	−	0.508463i	−0.681088	−	0.732201i	$-0.738493\pi$
$883$	8.72326	−	15.1091i	0.293561	−	0.508463i	0.974649	+	0.223739i	$0.0718263\pi$
$884$	−0.875384	−	0.734534i	−0.0294423	−	0.0247051i
$885$	−21.4745	−	4.91358i	−0.721857	−	0.165168i
$886$	6.39481	+	36.2668i	0.214838	+	1.21841i
$887$	−41.5325	+	34.8499i	−1.39453	+	1.17015i	−0.431058	+	0.902324i	$0.641860\pi$
$887$	−41.5325	+	34.8499i	−1.39453	+	1.17015i	−0.963468	+	0.267823i	$0.913696\pi$
$888$	−9.75203	−	6.30597i	−0.327257	−	0.211615i
$889$	3.92831	−	1.42979i	0.131751	−	0.0479536i
$890$	10.8769			0.364596
$891$	−10.4675	−	13.1840i	−0.350675	−	0.441681i
$892$	−7.21530			−0.241586
$893$	−4.40402	+	1.60293i	−0.147375	+	0.0536400i
$894$	−6.02361	−	3.89506i	−0.201460	−	0.130270i
$895$	−0.869150	+	0.729303i	−0.0290525	+	0.0243779i
$896$	−8.87211	−	50.3162i	−0.296396	−	1.68095i
$897$	−7.20846	−	1.64937i	−0.240683	−	0.0550708i
$898$	12.8396	+	10.7737i	0.428462	+	0.359523i
$899$	3.56595	−	6.17641i	0.118931	−	0.205995i
$900$	9.17560	+	0.928140i	0.305853	+	0.0309380i
$901$	−2.68796	−	4.65569i	−0.0895491	−	0.155104i
$902$	−0.980730	+	5.56200i	−0.0326547	+	0.185194i
$903$	−33.7944	+	4.21650i	−1.12461	+	0.140316i
$904$	37.0021	+	13.4677i	1.23067	+	0.447928i
$905$	−22.4738	−	8.17979i	−0.747054	−	0.271906i
$906$	11.9048	−	28.1991i	0.395510	−	0.936851i
$907$	4.98078	−	28.2474i	0.165384	−	0.937939i	−0.783284	−	0.621665i	$-0.786457\pi$
$907$	4.98078	−	28.2474i	0.165384	−	0.937939i	0.948668	−	0.316275i	$-0.102432\pi$
$908$	−1.67917	−	2.90841i	−0.0557252	−	0.0965188i
$909$	14.1938	−	50.2402i	0.470779	−	1.66636i
$910$	2.71857	−	4.70871i	0.0901198	−	0.156092i
$911$	−21.7416	−	18.2433i	−0.720330	−	0.604429i	0.207146	−	0.978310i	$-0.433582\pi$
$911$	−21.7416	−	18.2433i	−0.720330	−	0.604429i	−0.927477	+	0.373881i	$0.878027\pi$
$912$	−6.94676	−	22.5640i	−0.230030	−	0.747168i
$913$	3.79471	+	21.5208i	0.125586	+	0.712236i
$914$	−9.80947	+	8.23112i	−0.324468	+	0.272261i
$915$	9.10934	−	4.66389i	0.301146	−	0.154184i
$916$	−12.5319	+	4.56122i	−0.414064	+	0.150707i
$917$	−29.8653			−0.986240
$918$	−12.3925	+	10.9009i	−0.409014	+	0.359783i
$919$	37.7786			1.24620			0.623101	−	0.782141i	$-0.285873\pi$
$919$	37.7786			1.24620			0.623101	+	0.782141i	$0.285873\pi$
$920$	12.2123	−	4.44491i	0.402627	−	0.146544i
$921$	−2.65576	+	52.6438i	−0.0875104	+	1.73467i
$922$	−29.3592	+	24.6353i	−0.966893	+	0.811320i
$923$	1.54996	+	8.79027i	0.0510176	+	0.289335i
$924$	7.11435	−	7.65917i	0.234045	−	0.251968i
$925$	−9.68860	−	8.12970i	−0.318559	−	0.267303i
$926$	7.39243	−	12.8041i	0.242930	−	0.420768i
$927$	39.2247	−	26.6811i	1.28831	−	0.876323i
$928$	−11.7166	−	20.2937i	−0.384615	−	0.666173i
$929$	−6.00421	+	34.0516i	−0.196992	+	1.11720i	0.712562	+	0.701609i	$0.247535\pi$
$929$	−6.00421	+	34.0516i	−0.196992	+	1.11720i	−0.909554	+	0.415586i	$0.863576\pi$
$930$	2.66009	+	3.51573i	0.0872277	+	0.115285i
$931$	−21.3404	−	7.76726i	−0.699403	−	0.254562i
$932$	−13.3520	−	4.85972i	−0.437358	−	0.159185i
$933$	14.6265	+	19.3312i	0.478849	+	0.632877i
$934$	−3.21005	+	18.2051i	−0.105036	+	0.595688i
$935$	−1.99618	−	3.45749i	−0.0652822	−	0.113072i
$936$	3.90735	+	1.88687i	0.127716	+	0.0616741i
$937$	9.71839	−	16.8328i	0.317486	−	0.549902i	−0.662477	−	0.749082i	$-0.730495\pi$
$937$	9.71839	−	16.8328i	0.317486	−	0.549902i	0.979963	+	0.199180i	$0.0638280\pi$
$938$	9.50812	+	7.97826i	0.310451	+	0.260499i
$939$	26.0363	−	28.0302i	0.849663	−	0.914731i
$940$	−0.276651	−	1.56897i	−0.00902337	−	0.0511741i
$941$	7.61330	−	6.38832i	0.248187	−	0.208253i	−0.510204	−	0.860053i	$-0.670430\pi$
$941$	7.61330	−	6.38832i	0.248187	−	0.208253i	0.758391	+	0.651800i	$0.225986\pi$
$942$	0.0528003	−	1.04663i	0.00172033	−	0.0341011i
$943$	9.83716	−	3.58043i	0.320342	−	0.116595i
$944$	55.9572			1.82125
$945$	−17.9141	−	14.3334i	−0.582746	−	0.466266i
$946$	−15.8152			−0.514195
$947$	−15.8909	+	5.78380i	−0.516384	+	0.187948i	−0.587048	−	0.809552i	$-0.699710\pi$
$947$	−15.8909	+	5.78380i	−0.516384	+	0.187948i	0.0706647	+	0.997500i	$0.477488\pi$
$948$	−15.7208	+	8.04890i	−0.510588	+	0.261416i
$949$	−5.54899	+	4.65616i	−0.180128	+	0.151145i
$950$	−2.98156	−	16.9093i	−0.0967345	−	0.548609i
$951$	8.86198	+	28.7849i	0.287369	+	0.933413i
$952$	11.1712	+	9.37379i	0.362062	+	0.303806i
$953$	−8.67866	+	15.0319i	−0.281129	+	0.486930i	−0.971663	−	0.236370i	$-0.924042\pi$
$953$	−8.67866	+	15.0319i	−0.281129	+	0.486930i	0.690534	+	0.723300i	$0.257376\pi$
$954$	−10.0060	−	10.2808i	−0.323958	−	0.332854i
$955$	−5.55079	−	9.61426i	−0.179620	−	0.311110i
$956$	−0.220091	+	1.24820i	−0.00711825	+	0.0403696i
$957$	−6.70327	+	15.8782i	−0.216686	+	0.513268i
$958$	−40.5824	−	14.7708i	−1.31116	−	0.477222i
$959$	57.4872	+	20.9236i	1.85636	+	0.675659i
$960$	−4.92144	+	0.614045i	−0.158839	+	0.0198182i
$961$	−5.07101	+	28.7591i	−0.163581	+	0.927714i
$962$	2.09104	+	3.62179i	0.0674179	+	0.116771i
$963$	−20.3468	−	45.2230i	−0.655667	−	1.45729i
$964$	2.27898	−	3.94730i	0.0734009	−	0.127134i
$965$	9.65315	+	8.09995i	0.310746	+	0.260747i
$966$	−64.6515	−	14.7929i	−2.08013	−	0.475955i
$967$	−2.91440	−	16.5284i	−0.0937207	−	0.531517i	−0.995132	−	0.0985525i	$-0.968579\pi$
$967$	−2.91440	−	16.5284i	−0.0937207	−	0.531517i	0.901411	−	0.432964i	$-0.142532\pi$
$968$	11.3451	−	9.51963i	0.364644	−	0.305973i
$969$	7.53850	+	4.87464i	0.242172	+	0.156596i
$970$	−0.612642	+	0.222984i	−0.0196708	+	0.00715957i
$971$	−33.4811			−1.07446			−0.537230	−	0.843436i	$-0.680529\pi$
$971$	−33.4811			−1.07446			−0.537230	+	0.843436i	$0.680529\pi$
$972$	−7.27725	+	10.6123i	−0.233418	+	0.340389i
$973$	−33.8393			−1.08484
$974$	47.9865	−	17.4657i	1.53759	−	0.559636i
$975$	3.96819	+	2.56596i	0.127084	+	0.0821765i
$976$	−19.9134	+	16.7093i	−0.637413	+	0.534853i
$977$	3.94786	+	22.3894i	0.126303	+	0.716302i	0.980525	+	0.196393i	$0.0629229\pi$
$977$	3.94786	+	22.3894i	0.126303	+	0.716302i	−0.854222	+	0.519909i	$0.825966\pi$
$978$	−41.4887	−	9.49303i	−1.32666	−	0.303554i
$979$	8.20843	+	6.88769i	0.262342	+	0.220131i
$980$	3.85998	−	6.68569i	0.123303	−	0.213567i
$981$	−5.80800	−	12.9089i	−0.185435	−	0.412150i
$982$	−7.31892	−	12.6767i	−0.233556	−	0.404531i
$983$	8.18917	−	46.4431i	0.261194	−	1.48131i	−0.518464	−	0.855100i	$-0.673496\pi$
$983$	8.18917	−	46.4431i	0.261194	−	1.48131i	0.779658	−	0.626206i	$-0.215393\pi$
$984$	−6.09542	+	0.760522i	−0.194315	+	0.0242445i
$985$	9.64828	+	3.51169i	0.307420	+	0.111892i
$986$	15.8788	+	5.77940i	0.505683	+	0.184054i
$987$	4.49936	−	10.6577i	0.143216	−	0.339238i
$988$	−0.288030	+	1.63350i	−0.00916346	+	0.0519686i
$989$	14.6571	+	25.3869i	0.466069	+	0.807255i
$990$	−7.43087	−	7.63493i	−0.236169	−	0.242654i
$991$	2.18837	−	3.79036i	0.0695158	−	0.120405i	−0.829172	−	0.558993i	$-0.811188\pi$
$991$	2.18837	−	3.79036i	0.0695158	−	0.120405i	0.898688	+	0.438588i	$0.144521\pi$
$992$	−4.52353	−	3.79569i	−0.143622	−	0.120513i
$993$	0.440404	+	1.43049i	0.0139758	+	0.0453952i
$994$	13.9014	+	78.8386i	0.440925	+	2.50061i
$995$	12.7143	−	10.6686i	0.403072	−	0.338217i
$996$	14.8685	−	7.61253i	0.471127	−	0.241212i
$997$	2.01517	−	0.733462i	0.0638211	−	0.0232290i	−0.309912	−	0.950765i	$-0.600300\pi$
$997$	2.01517	−	0.733462i	0.0638211	−	0.0232290i	0.373733	+	0.927536i	$0.378077\pi$
$998$	19.5582			0.619104
$999$	16.4373	−	6.42052i	0.520052	−	0.203136i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.2.e.a.7.1	yes	12
3.2	odd	2		81.2.e.a.19.2		12
4.3	odd	2		432.2.u.c.385.1		12
5.2	odd	4		675.2.u.b.574.1		24
5.3	odd	4		675.2.u.b.574.4		24
5.4	even	2		675.2.l.c.601.2		12
9.2	odd	6		243.2.e.a.136.1		12
9.4	even	3		243.2.e.c.217.2		12
9.5	odd	6		243.2.e.b.217.1		12
9.7	even	3		243.2.e.d.136.2		12
27.2	odd	18		729.2.a.d.1.1		6
27.4	even	9	inner	27.2.e.a.4.1	✓	12
27.5	odd	18		243.2.e.b.28.1		12
27.7	even	9		729.2.c.e.487.1		12
27.11	odd	18		729.2.c.b.244.6		12
27.13	even	9		243.2.e.d.109.2		12
27.14	odd	18		243.2.e.a.109.1		12
27.16	even	9		729.2.c.e.244.1		12
27.20	odd	18		729.2.c.b.487.6		12
27.22	even	9		243.2.e.c.28.2		12
27.23	odd	18		81.2.e.a.64.2		12
27.25	even	9		729.2.a.a.1.6		6
108.31	odd	18		432.2.u.c.193.1		12
135.4	even	18		675.2.l.c.301.2		12
135.58	odd	36		675.2.u.b.274.1		24
135.112	odd	36		675.2.u.b.274.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.4.1	✓	12	27.4	even	9	inner
27.2.e.a.7.1	yes	12	1.1	even	1	trivial
81.2.e.a.19.2		12	3.2	odd	2
81.2.e.a.64.2		12	27.23	odd	18
243.2.e.a.109.1		12	27.14	odd	18
243.2.e.a.136.1		12	9.2	odd	6
243.2.e.b.28.1		12	27.5	odd	18
243.2.e.b.217.1		12	9.5	odd	6
243.2.e.c.28.2		12	27.22	even	9
243.2.e.c.217.2		12	9.4	even	3
243.2.e.d.109.2		12	27.13	even	9
243.2.e.d.136.2		12	9.7	even	3
432.2.u.c.193.1		12	108.31	odd	18
432.2.u.c.385.1		12	4.3	odd	2
675.2.l.c.301.2		12	135.4	even	18
675.2.l.c.601.2		12	5.4	even	2
675.2.u.b.274.1		24	135.58	odd	36
675.2.u.b.274.4		24	135.112	odd	36
675.2.u.b.574.1		24	5.2	odd	4
675.2.u.b.574.4		24	5.3	odd	4
729.2.a.a.1.6		6	27.25	even	9
729.2.a.d.1.1		6	27.2	odd	18
729.2.c.b.244.6		12	27.11	odd	18
729.2.c.b.487.6		12	27.20	odd	18
729.2.c.e.244.1		12	27.16	even	9
729.2.c.e.487.1		12	27.7	even	9

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	27.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.57954 + 0.574906i) q^{2} +(1.45446 + 0.940501i) q^{3} +(0.632343 - 0.530599i) q^{4} +(-0.196143 - 1.11238i) q^{5} +(-2.83808 - 0.649381i) q^{6} +(-2.99441 - 2.51261i) q^{7} +(0.987144 - 1.70978i) q^{8} +(1.23092 + 2.73584i) q^{9} +O(q^{10})\)	\(q+(-1.57954 + 0.574906i) q^{2} +(1.45446 + 0.940501i) q^{3} +(0.632343 - 0.530599i) q^{4} +(-0.196143 - 1.11238i) q^{5} +(-2.83808 - 0.649381i) q^{6} +(-2.99441 - 2.51261i) q^{7} +(0.987144 - 1.70978i) q^{8} +(1.23092 + 2.73584i) q^{9} +(0.949332 + 1.64429i) q^{10} +(-0.324801 + 1.84204i) q^{11} +(1.41875 - 0.177016i) q^{12} +(0.688417 + 0.250563i) q^{13} +(6.17430 + 2.24726i) q^{14} +(0.760915 - 1.80239i) q^{15} +(-0.862951 + 4.89404i) q^{16} +(-0.944822 - 1.63648i) q^{17} +(-3.51713 - 3.61372i) q^{18} +(-1.37143 + 2.37538i) q^{19} +(-0.714260 - 0.599335i) q^{20} +(-1.99214 - 6.47073i) q^{21} +(-0.545962 - 3.09631i) q^{22} +(-4.46428 + 3.74597i) q^{23} +(3.04382 - 1.55840i) q^{24} +(3.49954 - 1.27373i) q^{25} -1.23143 q^{26} +(-0.782746 + 5.13686i) q^{27} -3.22668 q^{28} +(4.99910 - 1.81953i) q^{29} +(-0.165691 + 3.28441i) q^{30} +(1.02696 - 0.861722i) q^{31} +(-0.764882 - 4.33786i) q^{32} +(-2.20485 + 2.37370i) q^{33} +(2.43321 + 2.04170i) q^{34} +(-2.20765 + 3.82376i) q^{35} +(2.23000 + 1.07687i) q^{36} +(-1.69806 - 2.94112i) q^{37} +(0.800605 - 4.54046i) q^{38} +(0.765621 + 1.01189i) q^{39} +(-2.09556 - 0.762721i) q^{40} +(-1.68800 - 0.614382i) q^{41} +(6.86673 + 9.07549i) q^{42} +(0.873477 - 4.95373i) q^{43} +(0.771999 + 1.33714i) q^{44} +(2.80187 - 1.90587i) q^{45} +(4.89793 - 8.48346i) q^{46} +(1.30892 + 1.09832i) q^{47} +(-5.85798 + 6.30658i) q^{48} +(1.43775 + 8.15389i) q^{49} +(-4.79539 + 4.02381i) q^{50} +(0.164904 - 3.26880i) q^{51} +(0.568265 - 0.206831i) q^{52} +2.84494 q^{53} +(-1.71683 - 8.56388i) q^{54} +2.11276 q^{55} +(-7.25193 + 2.63949i) q^{56} +(-4.22874 + 2.16507i) q^{57} +(-6.85023 + 5.74803i) q^{58} +(-1.95529 - 11.0890i) q^{59} +(-0.475188 - 1.54347i) q^{60} +(4.00710 + 3.36235i) q^{61} +(-1.12672 + 1.95153i) q^{62} +(3.18824 - 11.2850i) q^{63} +(-1.26751 - 2.19540i) q^{64} +(0.143694 - 0.814930i) q^{65} +(2.11800 - 5.01694i) q^{66} +(1.77511 + 0.646086i) q^{67} +(-1.46577 - 0.533495i) q^{68} +(-10.0162 + 1.24972i) q^{69} +(1.28877 - 7.30898i) q^{70} +(6.09193 + 10.5515i) q^{71} +(5.89280 + 0.596074i) q^{72} +(-4.94384 + 8.56298i) q^{73} +(4.37302 + 3.66940i) q^{74} +(6.28788 + 1.43873i) q^{75} +(0.393163 + 2.22974i) q^{76} +(5.60091 - 4.69972i) q^{77} +(-1.79107 - 1.15816i) q^{78} +(-11.6079 + 4.22493i) q^{79} +5.61331 q^{80} +(-5.96969 + 6.73519i) q^{81} +3.01948 q^{82} +(10.9786 - 3.99588i) q^{83} +(-4.69308 - 3.03470i) q^{84} +(-1.63507 + 1.37199i) q^{85} +(1.46824 + 8.32679i) q^{86} +(8.98227 + 2.05523i) q^{87} +(2.82886 + 2.37370i) q^{88} +(2.86437 - 4.96123i) q^{89} +(-3.32998 + 4.62121i) q^{90} +(-1.43183 - 2.48001i) q^{91} +(-0.835346 + 4.73748i) q^{92} +(2.30412 - 0.287484i) q^{93} +(-2.69893 - 0.982329i) q^{94} +(2.91133 + 1.05964i) q^{95} +(2.96727 - 7.02862i) q^{96} +(-0.0596270 + 0.338162i) q^{97} +(-6.95870 - 12.0528i) q^{98} +(-5.43934 + 1.37879i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) \) 12 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 6 * q^8	\( 12 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 6 q^{8} - 3 q^{10} + 3 q^{11} + 12 q^{12} - 6 q^{13} + 15 q^{14} + 9 q^{15} + 9 q^{17} + 9 q^{18} - 3 q^{19} - 3 q^{20} - 12 q^{21} + 3 q^{22} - 12 q^{23} - 18 q^{24} + 3 q^{25} - 30 q^{26} - 9 q^{27} - 12 q^{28} - 6 q^{29} - 9 q^{30} + 3 q^{31} + 9 q^{34} + 12 q^{35} + 18 q^{36} - 3 q^{37} + 42 q^{38} + 33 q^{39} + 21 q^{40} + 15 q^{41} + 18 q^{42} + 3 q^{43} + 3 q^{44} - 9 q^{45} - 3 q^{46} - 15 q^{47} - 15 q^{48} + 12 q^{49} - 33 q^{50} - 18 q^{51} + 9 q^{52} - 18 q^{53} - 54 q^{54} - 12 q^{55} - 33 q^{56} - 3 q^{57} + 21 q^{58} - 12 q^{59} + 12 q^{61} - 12 q^{62} + 9 q^{63} + 12 q^{64} + 3 q^{65} - 9 q^{66} - 15 q^{67} + 9 q^{68} + 9 q^{69} - 15 q^{70} + 27 q^{71} + 18 q^{72} + 6 q^{73} + 33 q^{74} + 39 q^{75} - 48 q^{76} + 15 q^{77} + 18 q^{78} - 42 q^{79} + 42 q^{80} + 36 q^{81} - 12 q^{82} + 39 q^{83} + 6 q^{84} - 27 q^{85} + 51 q^{86} + 9 q^{87} - 30 q^{88} + 9 q^{89} + 18 q^{90} + 6 q^{91} - 39 q^{92} - 39 q^{93} - 15 q^{94} - 33 q^{95} + 3 q^{97} - 45 q^{98} - 27 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 6 * q^8 - 3 * q^10 + 3 * q^11 + 12 * q^12 - 6 * q^13 + 15 * q^14 + 9 * q^15 + 9 * q^17 + 9 * q^18 - 3 * q^19 - 3 * q^20 - 12 * q^21 + 3 * q^22 - 12 * q^23 - 18 * q^24 + 3 * q^25 - 30 * q^26 - 9 * q^27 - 12 * q^28 - 6 * q^29 - 9 * q^30 + 3 * q^31 + 9 * q^34 + 12 * q^35 + 18 * q^36 - 3 * q^37 + 42 * q^38 + 33 * q^39 + 21 * q^40 + 15 * q^41 + 18 * q^42 + 3 * q^43 + 3 * q^44 - 9 * q^45 - 3 * q^46 - 15 * q^47 - 15 * q^48 + 12 * q^49 - 33 * q^50 - 18 * q^51 + 9 * q^52 - 18 * q^53 - 54 * q^54 - 12 * q^55 - 33 * q^56 - 3 * q^57 + 21 * q^58 - 12 * q^59 + 12 * q^61 - 12 * q^62 + 9 * q^63 + 12 * q^64 + 3 * q^65 - 9 * q^66 - 15 * q^67 + 9 * q^68 + 9 * q^69 - 15 * q^70 + 27 * q^71 + 18 * q^72 + 6 * q^73 + 33 * q^74 + 39 * q^75 - 48 * q^76 + 15 * q^77 + 18 * q^78 - 42 * q^79 + 42 * q^80 + 36 * q^81 - 12 * q^82 + 39 * q^83 + 6 * q^84 - 27 * q^85 + 51 * q^86 + 9 * q^87 - 30 * q^88 + 9 * q^89 + 18 * q^90 + 6 * q^91 - 39 * q^92 - 39 * q^93 - 15 * q^94 - 33 * q^95 + 3 * q^97 - 45 * q^98 - 27 * q^99

Introduction

L-functions

Modular forms

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